Explanation: A research hypothesis is a statement that provides a relationship between two or more variables. It is an educated guess that can be tested through experiments or observations in research.
2. Which of the following is true about a null hypothesis?
(A) It predicts a relationship between variables
(B) It is always proven true
(C) It supports the alternative hypothesis
(D) It states that there is no effect or no relationship
(D) It states that there is no effect or no relationship
Explanation: A null hypothesis (H₀) posits that there is no effect or no relationship between the variables being studied. It serves as a baseline that researchers attempt to disprove or reject.
3. A research hypothesis must be:
(A) Specific and testable
(B) General and untestable
(C) Broad and untestable
(D) Based on subjective opinions
(A) Specific and testable
Explanation: A good research hypothesis should be specific and testable, meaning it can be supported or refuted through experimentation or observation.
4. In hypothesis testing, a p-value is used to:
(A) Measure the size of the sample
(B) Determine the effect size
(C) Test the null hypothesis
(D) Identify the research method
(C) Test the null hypothesis
Explanation: The p-value helps determine whether the null hypothesis can be rejected. A low p-value indicates strong evidence against the null hypothesis, while a high p-value suggests that the null hypothesis cannot be rejected.
5. Which of the following is a characteristic of a good hypothesis?
(A) It is vague and open to multiple interpretations
(B) It can be tested through experiments or observations
(C) It is difficult to falsify
(D) It is based on intuition and personal opinion
(B) It can be tested through experiments or observations
Explanation: A good hypothesis must be testable, meaning it can be supported or refuted by experimentation or observation. It should be clear and specific enough to guide the research process.
6. In research, a hypothesis is often derived from:
(A) The researcher's personal beliefs
(B) The hypothesis testing process itself
(C) Random speculation
(D) Previous studies or literature
(D) Previous studies or literature
Explanation: Hypotheses are often generated based on a review of existing literature, research gaps, or theories. This ensures that the hypothesis is grounded in prior knowledge and can be tested effectively.
7. Which of the following is NOT a type of hypothesis?
(A) Descriptive hypothesis
(B) Analytical hypothesis
(C) Statistical hypothesis
(D) Causal hypothesis
(B) Analytical hypothesis
Explanation: Analytical hypotheses are not typically classified as a distinct type. Common types of hypotheses include descriptive, statistical, and causal hypotheses, each serving different research purposes.
8. What does a directional hypothesis specify?
(A) The direction of the relationship between variables
(B) The sample size needed for the study
(C) The methods used for data collection
(D) The hypothesis testing procedure
(A) The direction of the relationship between variables
Explanation: A directional hypothesis specifies not only that a relationship exists but also the direction of the relationship (e.g., positive or negative). This contrasts with a non-directional hypothesis, which only states that a relationship exists without specifying its direction.
9. In hypothesis testing, what does it mean if the p-value is less than 0.05?
(A) The null hypothesis is accepted
(B) The null hypothesis is rejected
(C) The research hypothesis is proven
(D) The sample size is too small
(B) The null hypothesis is rejected
Explanation: If the p-value is less than 0.05, it indicates that the result is statistically significant, meaning there is strong evidence against the null hypothesis, and it can be rejected in favor of the alternative hypothesis.
10. A hypothesis that suggests a cause-and-effect relationship is known as a:
(A) Descriptive hypothesis
(B) Null hypothesis
(C) Correlational hypothesis
(D) Causal hypothesis
(D) Causal hypothesis
Explanation: A causal hypothesis proposes that one variable causes an effect in another variable. It is often tested through experiments to establish cause-and-effect relationships.
11. Which of the following is an example of a non-directional hypothesis?
(A) There is a positive relationship between hours of study and academic performance.
(B) There is a relationship between hours of study and academic performance.
(C) Increased study hours will decrease academic performance.
(D) None of the above
(B) There is a relationship between hours of study and academic performance.
Explanation: A non-directional hypothesis simply states that a relationship exists between two variables but does not specify whether the relationship is positive or negative.
12. A hypothesis that is stated in terms of an expected relationship between variables is called a:
(A) Descriptive hypothesis
(B) Statistical hypothesis
(C) Research hypothesis
(D) Null hypothesis
(C) Research hypothesis
Explanation: A research hypothesis is a testable statement that predicts the relationship between two or more variables. It provides a direction for the research and guides data collection and analysis.
13. The process of rejecting the null hypothesis when it is actually true is called:
(A) Type I error
(B) Type II error
(C) Statistical significance
(D) Power of the test
(A) Type I error
Explanation: A Type I error occurs when the null hypothesis is rejected even though it is true. This is also known as a "false positive."
14. A hypothesis is considered to be falsifiable if:
(A) It can be supported by evidence
(B) It can be tested and potentially proven wrong
(C) It is based on personal beliefs
(D) It is impossible to test
(B) It can be tested and potentially proven wrong
Explanation: A hypothesis is considered falsifiable if it can be tested and possibly disproven through experimentation or observation, which is a key aspect of scientific research.
15. What is the role of a hypothesis in the scientific method?
(A) To guide the design of experiments or observations
(B) To provide a theory that explains observed phenomena
(C) To state the final conclusions of a study
(D) To summarize the findings of the research
(A) To guide the design of experiments or observations
Explanation: A hypothesis serves as the foundation for experimental design. It suggests a possible outcome that can be tested and examined through data collection and analysis.
16. Which of the following is an example of a directional hypothesis?
(A) There is a relationship between exercise and weight loss.
(B) Exercise has a positive effect on weight loss.
(C) There is no relationship between exercise and weight loss.
(D) Exercise has no effect on weight loss.
(B) Exercise has a positive effect on weight loss.
Explanation: A directional hypothesis specifies the direction of the relationship between variables (in this case, a positive effect of exercise on weight loss). It predicts not only that a relationship exists, but also its direction.
17. In hypothesis testing, what is the alternative hypothesis?
(A) It suggests that there is no relationship between the variables
(B) It is the hypothesis that is rejected in favor of the null hypothesis
(C) It suggests that there is a relationship between the variables
(D) It is always accepted
(C) It suggests that there is a relationship between the variables
Explanation: The alternative hypothesis (H₁) suggests that there is a significant relationship between the variables being studied. It is considered when the null hypothesis is rejected.
18. A hypothesis that assumes no effect or relationship between variables is called:
(A) Null hypothesis
(B) Research hypothesis
(C) Alternative hypothesis
(D) Directional hypothesis
(A) Null hypothesis
Explanation: The null hypothesis (H₀) assumes that there is no effect or no relationship between the variables being studied. It serves as a baseline that researchers attempt to disprove.
19. Which of the following is a characteristic of a good research hypothesis?
(A) It is based on existing knowledge and theories
(B) It is too general to be tested
(C) It cannot be tested or measured
(D) It is based solely on intuition
(A) It is based on existing knowledge and theories
Explanation: A good research hypothesis is grounded in existing knowledge, theories, or previous research. It should be testable, specific, and based on evidence.
20. The power of a statistical test refers to:
(A) The probability of committing a Type I error
(B) The probability of committing a Type II error
(C) The probability of detecting an effect if it exists
(D) The number of samples in the study
(C) The probability of detecting an effect if it exists
Explanation: The power of a statistical test is the probability that it will correctly reject the null hypothesis when the alternative hypothesis is true. High power increases the likelihood of detecting a true effect.
21. In hypothesis testing, which of the following is used to assess whether the observed data is consistent with the null hypothesis?
(A) P-value
(B) Effect size
(C) Confidence interval
(D) Sample size
(A) P-value
Explanation: The p-value is used to assess the strength of evidence against the null hypothesis. A low p-value (usually less than 0.05) indicates strong evidence against the null hypothesis, suggesting that it can be rejected.
22. Which of the following statements is true about the alternative hypothesis?
(A) It suggests that there is no effect or relationship between the variables
(B) It is the hypothesis that is accepted when the null hypothesis is rejected
(C) It is always rejected if the p-value is less than 0.05
(D) It cannot be tested
(B) It is the hypothesis that is accepted when the null hypothesis is rejected
Explanation: The alternative hypothesis is accepted when the null hypothesis is rejected, typically when the p-value is small, suggesting evidence against the null hypothesis.
23. What type of hypothesis would you use if you were testing a specific relationship between two variables, such as "more study hours lead to higher test scores"?
(A) Non-directional hypothesis
(B) Causal hypothesis
(C) Statistical hypothesis
(D) Directional hypothesis
(D) Directional hypothesis
Explanation: A directional hypothesis specifies not only the presence of a relationship between variables but also the direction of the relationship, such as "more study hours lead to higher test scores."
24. A hypothesis that is based on a theory and aims to explain the relationship between variables is referred to as:
(A) Descriptive hypothesis
(B) Experimental hypothesis
(C) Causal hypothesis
(D) Theoretical hypothesis
(D) Theoretical hypothesis
Explanation: A theoretical hypothesis is based on an existing theory and seeks to explain the relationship between variables according to that theory.
25. Which of the following is an example of a null hypothesis?
(A) There is a positive correlation between physical activity and mental health.
(B) There is no relationship between physical activity and mental health.
(C) Physical activity improves mental health.
(D) Physical activity reduces stress levels.
(B) There is no relationship between physical activity and mental health.
Explanation: The null hypothesis generally assumes that there is no effect or relationship between the variables being tested, such as "There is no relationship between physical activity and mental health."
26. In hypothesis testing, which of the following errors occurs when the null hypothesis is not rejected when it is false?
(A) Type I error
(B) Type II error
(C) Statistical significance error
(D) Measurement error
(B) Type II error
Explanation: A Type II error occurs when the null hypothesis is not rejected, even though it is false. This is also known as a "false negative."
27. A hypothesis that suggests that an increase in one variable leads to an increase in another variable is an example of a:
(A) Causal hypothesis
(B) Directional hypothesis
(C) Negative correlation hypothesis
(D) Positive correlation hypothesis
(D) Positive correlation hypothesis
Explanation: A positive correlation hypothesis suggests that as one variable increases, the other also increases, which is a positive relationship between the two variables.
28. The null hypothesis is typically stated in terms of:
(A) A specific relationship between variables
(B) A general relationship between variables
(C) The absence of a relationship between variables
(D) A directional relationship between variables
(C) The absence of a relationship between variables
Explanation: The null hypothesis generally assumes that there is no effect or relationship between the variables, which is the baseline against which the alternative hypothesis is tested.
29. Which of the following best defines the concept of a hypothesis in research?
(A) A conclusion based on observed data
(B) An educated guess or prediction that can be tested
(C) A result derived from data analysis
(D) A description of the research process
(B) An educated guess or prediction that can be tested
Explanation: A hypothesis is an educated guess or prediction about the relationship between variables that can be tested through experimentation or observation.
30. What is the purpose of hypothesis testing in research?
(A) To confirm the researcher's beliefs
(B) To prove the research hypothesis is true
(C) To test the validity of the null hypothesis
(D) To summarize the data findings
(C) To test the validity of the null hypothesis
Explanation: The purpose of hypothesis testing is to assess the validity of the null hypothesis. Researchers use statistical methods to determine if there is sufficient evidence to reject the null hypothesis in favor of the alternative hypothesis.
31. A hypothesis that predicts no significant relationship between the variables is called:
(A) Null hypothesis
(B) Research hypothesis
(C) Causal hypothesis
(D) Alternative hypothesis
(A) Null hypothesis
Explanation: The null hypothesis predicts no significant relationship or effect between the variables. It serves as the baseline that is tested to see if the alternative hypothesis can be supported.
32. Which of the following is an example of a directional hypothesis?
(A) There is a relationship between job satisfaction and productivity.
(B) Increased exercise leads to reduced stress levels.
(C) There is no relationship between study hours and exam scores.
(D) More sleep improves cognitive performance.
(B) Increased exercise leads to reduced stress levels.
Explanation: A directional hypothesis specifies the nature of the relationship between variables, in this case, suggesting that increased exercise leads to reduced stress levels.
33. A hypothesis is considered to be statistically significant if:
(A) The p-value is greater than 0.05
(B) The p-value is less than 0.05
(C) The sample size is very large
(D) The hypothesis is directional
(B) The p-value is less than 0.05
Explanation: A p-value less than 0.05 typically indicates that the results are statistically significant, meaning there is strong evidence to reject the null hypothesis.
34. Which of the following is NOT a characteristic of a good hypothesis?
(A) It should be testable through experimentation
(B) It should be based on previous research or theory
(C) It should be vague and not specific
(D) It should be clear and precise
(C) It should be vague and not specific
Explanation: A good hypothesis should be clear, specific, and testable. Vague hypotheses cannot be tested effectively and do not provide clear guidance for research.
35. A hypothesis that suggests a relationship between two or more variables is known as:
(A) Descriptive hypothesis
(B) Analytical hypothesis
(C) Correlational hypothesis
(D) Experimental hypothesis
(C) Correlational hypothesis
Explanation: A correlational hypothesis suggests a relationship or correlation between two or more variables but does not specify the cause-and-effect nature of the relationship.
36. A hypothesis that is proven or disproven through statistical testing is known as a:
(A) Descriptive hypothesis
(B) Null hypothesis
(C) Research hypothesis
(D) Statistical hypothesis
(D) Statistical hypothesis
Explanation: A statistical hypothesis is one that can be tested using statistical methods to either accept or reject the hypothesis based on the data collected.
37. Which of the following is an example of a causal hypothesis?
(A) There is a correlation between exercise and weight loss.
(B) Smoking causes lung cancer.
(C) Higher income is associated with better health.
(D) There is a relationship between education level and career success.
(B) Smoking causes lung cancer.
Explanation: A causal hypothesis suggests that one variable causes a change in another. "Smoking causes lung cancer" implies a cause-and-effect relationship.
38. In hypothesis testing, what does the term "power" refer to?
(A) The likelihood of correctly rejecting the null hypothesis when it is false
(B) The likelihood of rejecting the null hypothesis when it is true
(C) The strength of the statistical test used
(D) The sample size of the study
(A) The likelihood of correctly rejecting the null hypothesis when it is false
Explanation: The power of a statistical test is the probability of correctly rejecting the null hypothesis when it is false. A higher power reduces the chance of committing a Type II error.
39. What is the primary difference between a directional hypothesis and a non-directional hypothesis?
(A) Directional hypotheses are not testable, whereas non-directional ones are.
(B) Directional hypotheses predict the direction of the relationship, while non-directional hypotheses do not.
(C) Directional hypotheses are always rejected.
(D) Non-directional hypotheses predict no relationship.
(B) Directional hypotheses predict the direction of the relationship, while non-directional hypotheses do not.
Explanation: A directional hypothesis predicts not only that a relationship exists but also the direction (positive or negative), while a non-directional hypothesis only states that a relationship exists without specifying the direction.
40. What is a Type II error in hypothesis testing?
(A) Rejecting the null hypothesis when it is true
(B) Accepting the alternative hypothesis when it is false
(C) Accepting the null hypothesis when it is false
(D) Failing to reject the null hypothesis when it is false
(D) Failing to reject the null hypothesis when it is false
Explanation: A Type II error occurs when the null hypothesis is not rejected, even though it is false. This is also known as a "false negative."
41. What is a one-tailed test in hypothesis testing?
(A) A test that tests the hypothesis in one direction only (either positive or negative)
(B) A test that tests the hypothesis in both directions (positive and negative)
(C) A test that cannot reject the null hypothesis
(D) A test that always supports the null hypothesis
(A) A test that tests the hypothesis in one direction only (either positive or negative)
Explanation: A one-tailed test tests the hypothesis in only one direction, either looking for a positive or negative effect. It is used when the research predicts a specific direction for the effect.
42. Which of the following best defines a research hypothesis?
(A) A statement that predicts the relationship between variables
(B) A testable statement about a population
(C) A theory that explains a phenomenon
(D) A conclusion based on statistical analysis
(A) A statement that predicts the relationship between variables
Explanation: A research hypothesis is a statement that predicts the relationship between two or more variables. It is the guiding principle of research and can be tested through experimentation or observation.
43. What is the difference between a null hypothesis and an alternative hypothesis?
(A) The null hypothesis states that there is no effect or relationship, while the alternative hypothesis suggests that there is a relationship.
(B) The null hypothesis is always accepted, while the alternative hypothesis is always rejected.
(C) The null hypothesis is based on intuition, while the alternative hypothesis is based on facts.
(D) The null hypothesis and alternative hypothesis are essentially the same.
(A) The null hypothesis states that there is no effect or relationship, while the alternative hypothesis suggests that there is a relationship.
Explanation: The null hypothesis assumes no effect or relationship between variables. The alternative hypothesis suggests that there is a significant relationship or effect between the variables being studied.
44. Which of the following is an example of a two-tailed test?
(A) Testing if a drug increases heart rate
(B) Testing if a drug affects heart rate, either increasing or decreasing it
(C) Testing if heart rate is affected by exercise
(D) Testing if a new teaching method improves test scores
(B) Testing if a drug affects heart rate, either increasing or decreasing it
Explanation: A two-tailed test tests for the possibility of an effect in both directions. It checks if the drug increases or decreases heart rate, rather than only one of these effects.
45. In hypothesis testing, what does statistical significance indicate?
(A) The hypothesis is true
(B) The sample size is large enough to support the hypothesis
(C) The observed result is unlikely to have occurred by chance
(D) The null hypothesis is always accepted
(C) The observed result is unlikely to have occurred by chance
Explanation: Statistical significance means that the observed result is unlikely to have occurred due to random chance alone. It suggests that the findings are reliable and that the null hypothesis can be rejected.
46. What is a confidence interval used for in hypothesis testing?
(A) To estimate the probability of a Type I error
(B) To provide a range of values within which the true population parameter is likely to fall
(C) To test the hypothesis directly
(D) To calculate the p-value
(B) To provide a range of values within which the true population parameter is likely to fall
Explanation: A confidence interval provides a range of values that is likely to contain the true population parameter with a certain level of confidence (e.g., 95% confidence).
47. What does it mean if a hypothesis is supported in hypothesis testing?
(A) The null hypothesis is rejected
(B) The null hypothesis is accepted
(C) The alternative hypothesis is rejected
(D) The results are inconclusive
(A) The null hypothesis is rejected
Explanation: If the hypothesis is supported, it means that there is enough evidence to reject the null hypothesis in favor of the alternative hypothesis, suggesting a significant relationship or effect between the variables.
48. What is a Type I error in hypothesis testing?
(A) Failing to reject the null hypothesis when it is false
(B) Rejecting the null hypothesis when it is true
(C) Accepting the alternative hypothesis when it is false
(D) Failing to detect a significant effect when one exists
(B) Rejecting the null hypothesis when it is true
Explanation: A Type I error occurs when the null hypothesis is rejected even though it is true. This is also known as a "false positive." It means that we wrongly conclude that there is an effect or relationship when there isn't.
49. In the context of hypothesis testing, what is effect size?
(A) The probability of making a Type II error
(B) The likelihood that the null hypothesis is true
(C) The sample size required for a valid test
(D) The strength or magnitude of the relationship between variables
(D) The strength or magnitude of the relationship between variables
Explanation: Effect size is a measure of the strength or magnitude of the relationship between variables. It helps in understanding the practical significance of the results, beyond statistical significance.
50. What is the first step in hypothesis testing?
(A) Conduct the experiment
(B) Determine the sample size
(C) Analyze the data
(D) Formulate the hypothesis
(B) Formulate the hypothesis
Explanation: The first step in hypothesis testing is to formulate the hypothesis, which involves predicting the relationship between the variables based on existing knowledge, theories, or observations.
51. What is the purpose of hypothesis testing in research?
(A) To prove that the hypothesis is true
(B) To validate the accuracy of the experimental design
(C) To determine the relationship between variables
(D) To provide evidence supporting the research hypothesis
(D) To provide evidence supporting the research hypothesis
Explanation: Hypothesis testing is used to assess whether there is enough statistical evidence to support the research hypothesis. It helps researchers determine whether their predictions are likely to be true based on the data collected.
52. What does a p-value of 0.01 indicate in hypothesis testing?
(A) The null hypothesis is true
(B) There is a 1% chance that the null hypothesis is true
(C) There is a 99% probability that the result is due to random chance
(D) The null hypothesis can be rejected with 99% confidence
(D) The null hypothesis can be rejected with 99% confidence
Explanation: A p-value of 0.01 indicates that there is only a 1% chance that the result occurred by random chance, which means there is strong evidence to reject the null hypothesis with 99% confidence.
53. Which of the following statements is true about the alternative hypothesis?
(A) It assumes no relationship between the variables
(B) It suggests a specific relationship between the variables
(C) It is always accepted if the null hypothesis is rejected
(D) It cannot be tested
(B) It suggests a specific relationship between the variables
Explanation: The alternative hypothesis suggests that there is a significant relationship or effect between the variables, which is tested against the null hypothesis.
54. What is the level of significance (α) in hypothesis testing?
(A) The probability of rejecting the null hypothesis when it is true
(B) The probability of making a Type II error
(C) The probability of accepting the null hypothesis when it is false
(D) The probability of failing to reject the null hypothesis when it is false
(A) The probability of rejecting the null hypothesis when it is true
Explanation: The level of significance (α) is the threshold for rejecting the null hypothesis. It is the probability of making a Type I error, or rejecting the null hypothesis when it is actually true. A common value for α is 0.05.
55. In hypothesis testing, a Type III error occurs when:
(A) The null hypothesis is accepted when it is false
(B) The alternative hypothesis is rejected when it is true
(C) The wrong hypothesis is tested in the first place
(D) The test statistic is incorrectly calculated
(C) The wrong hypothesis is tested in the first place
Explanation: A Type III error occurs when the researcher tests the wrong hypothesis. It involves addressing a different issue than the one intended, which can lead to misleading conclusions.
56. What is a two-tailed hypothesis test used for?
(A) To test if a relationship exists in a specific direction
(B) To test if a relationship exists, regardless of direction
(C) To test for equality between two groups
(D) To test if the null hypothesis is true
(B) To test if a relationship exists, regardless of direction
Explanation: A two-tailed test checks for the possibility of a relationship in either direction (positive or negative) between the variables. It is used when there is no specific prediction about the direction of the relationship.
57. In the context of hypothesis testing, what is the power of a test?
(A) The probability of rejecting the null hypothesis when it is true
(B) The probability of correctly rejecting the null hypothesis when it is false
(C) The strength of the effect observed
(D) The likelihood of making a Type II error
(B) The probability of correctly rejecting the null hypothesis when it is false
Explanation: The power of a test is the probability that it will correctly reject the null hypothesis when it is false. Higher power reduces the chances of making a Type II error.
58. What does it mean if a hypothesis is rejected in hypothesis testing?
(A) The null hypothesis is proven to be false
(B) The results are statistically insignificant
(C) There is insufficient evidence to support the research hypothesis
(D) The alternative hypothesis is accepted
(D) The alternative hypothesis is accepted
Explanation: When the null hypothesis is rejected, it means that there is enough evidence to support the alternative hypothesis, suggesting a significant relationship or effect.
59. Which of the following is a correct assumption of hypothesis testing?
(A) Data must be normally distributed
(B) Sample size must be large for all tests
(C) Only the null hypothesis is tested
(D) The sample must be chosen randomly
(D) The sample must be chosen randomly
Explanation: One assumption of hypothesis testing is that the sample must be randomly selected to ensure that the results are generalizable to the population.
60. In a one-tailed test, which of the following is tested?
(A) The direction of the relationship between the variables
(B) The strength of the relationship between the variables
(C) The equality of two variables
(D) Whether the null hypothesis is true
(A) The direction of the relationship between the variables
Explanation: A one-tailed test is used to test whether the relationship between the variables is in a specific direction (either positive or negative). It is suitable when there is a prior expectation about the direction of the effect.
61. What is a research hypothesis based on?
(A) Personal opinions
(B) Existing theories or literature
(C) Random guesses
(D) Conclusions from previous experiments
(B) Existing theories or literature
Explanation: A research hypothesis is typically based on existing theories, literature, or prior research. It builds on knowledge that has already been established in the field.
62. In hypothesis testing, which of the following is an assumption of the z-test?
(A) The data is normally distributed with a known population variance
(B) The sample size is small
(C) The data is not normally distributed
(D) The sample size must be greater than 30
(A) The data is normally distributed with a known population variance
Explanation: The z-test assumes that the data is normally distributed and that the population variance is known. It is used when the sample size is large, typically greater than 30.
63. Which of the following is a characteristic of a good hypothesis?
(A) It is too broad to test
(B) It is vague and unspecific
(C) It is testable and falsifiable
(D) It is based on personal beliefs
(C) It is testable and falsifiable
Explanation: A good hypothesis should be testable and falsifiable. This means that it can be tested through research, and it is possible to prove it wrong if the evidence contradicts it.
64. When performing a t-test, what is the primary assumption about the data?
(A) The data must be skewed
(B) The data must follow a normal distribution
(C) The sample size must be large
(D) The population variance is known
(B) The data must follow a normal distribution
Explanation: The t-test assumes that the data is normally distributed, especially when the sample size is small. It is used when the population variance is unknown.
65. In hypothesis testing, statistical significance is achieved when:
(A) The sample size is large
(B) The test is two-tailed
(C) The p-value is greater than 0.05
(D) The p-value is less than 0.05
(D) The p-value is less than 0.05
Explanation: Statistical significance is achieved when the p-value is less than 0.05, meaning that the result is unlikely to have occurred by random chance, and thus the null hypothesis can be rejected.
66. What is a confidence level in hypothesis testing?
(A) The probability that the hypothesis is correct
(B) The likelihood that the null hypothesis is true
(C) The percentage of times the true population parameter will fall within a confidence interval
(D) The likelihood of making a Type I error
(C) The percentage of times the true population parameter will fall within a confidence interval
Explanation: A confidence level represents the percentage of times that the true population parameter would fall within the confidence interval if the study were repeated multiple times (e.g., 95% confidence level means the true parameter would fall within the interval 95% of the time).
67. What is a one-tailed test most appropriate for?
(A) Testing a hypothesis where the effect is expected to go in one direction
(B) Testing a hypothesis without any expectation of direction
(C) Testing a hypothesis with a large sample size
(D) Testing for an equal effect in both directions
(A) Testing a hypothesis where the effect is expected to go in one direction
Explanation: A one-tailed test is used when the researcher predicts a specific direction for the effect (either positive or negative). It is not used when the effect could go in either direction.
68. What does a high p-value (e.g., > 0.05) suggest in hypothesis testing?
(A) Strong evidence to reject the null hypothesis
(B) Weak evidence to reject the null hypothesis
(C) Strong evidence to support the null hypothesis
(D) The sample size is too small
(B) Weak evidence to reject the null hypothesis
Explanation: A high p-value suggests that there is weak evidence against the null hypothesis, meaning that the null hypothesis cannot be rejected and the result is likely due to random chance.
69. What is a research hypothesis used to predict?
(A) The cause-and-effect relationship between variables
(B) The outcome of a single variable
(C) The correlation between two variables
(D) The null hypothesis
(A) The cause-and-effect relationship between variables
Explanation: A research hypothesis predicts the cause-and-effect relationship between variables. It suggests how changes in one variable may affect another.
70. What is the significance of a null hypothesis in hypothesis testing?
(A) It predicts the outcome of the research
(B) It must always be rejected if the research hypothesis is true
(C) It is always accepted if the p-value is high
(D) It serves as the default assumption that there is no effect or relationship
(D) It serves as the default assumption that there is no effect or relationship
Explanation: The null hypothesis serves as the default assumption in hypothesis testing, positing that there is no effect or relationship between the variables being studied. Researchers attempt to reject it in favor of the alternative hypothesis.
71. What does a Type II error in hypothesis testing refer to?
(A) Rejecting the null hypothesis when it is true
(B) Failing to reject the null hypothesis when it is false
(C) Accepting the alternative hypothesis when it is false
(D) Accepting the null hypothesis when it is true
(B) Failing to reject the null hypothesis when it is false
Explanation: A Type II error occurs when a false null hypothesis is not rejected. This is also known as a "false negative," where the test fails to detect an effect that actually exists.
72. What is the alternative hypothesis typically denoted by?
(A) H₀
(B) H1 or Ha
(C) H₂
(D) Hα
(B) H1 or Ha
Explanation: The alternative hypothesis is typically denoted by H₁ or Ha. It represents the statement that there is a significant relationship or effect between the variables being tested.
73. What is the critical value in hypothesis testing?
(A) The value that determines the probability of Type I error
(B) The value of the p-value that determines significance
(C) The value of the test statistic that corresponds to the sample mean
(D) The value used to compare the test statistic to determine whether to reject the null hypothesis
(D) The value used to compare the test statistic to determine whether to reject the null hypothesis
Explanation: The critical value is a threshold that determines whether the test statistic falls in the rejection region. If the test statistic is more extreme than the critical value, the null hypothesis is rejected.
74. When the p-value is smaller than the level of significance (α), what action should be taken?
(A) Reject the null hypothesis
(B) Fail to reject the null hypothesis
(C) Accept the alternative hypothesis
(D) Increase the sample size
(A) Reject the null hypothesis
Explanation: When the p-value is smaller than the level of significance (α), there is strong evidence against the null hypothesis, and it should be rejected in favor of the alternative hypothesis.
75. What is the term used for the probability of making a Type I error?
(A) Power of the test
(B) Level of significance (α)
(C) Confidence interval
(D) Effect size
(B) Level of significance (α)
Explanation: The probability of making a Type I error is denoted by the level of significance (α). It is the probability of rejecting the null hypothesis when it is actually true (i.e., a "false positive").
76. Which of the following is an example of a one-tailed test hypothesis?
(A) The new drug will reduce blood pressure
(B) The new drug will have an effect on blood pressure
(C) The new drug will increase blood pressure
(D) There will be no effect of the drug on blood pressure
(A) The new drug will reduce blood pressure
Explanation: A one-tailed test is used when the researcher predicts a specific direction of the effect. For example, "The new drug will reduce blood pressure" is a one-tailed hypothesis because it specifies a reduction.
77. What does the power of a test refer to?
(A) The ability to detect a false null hypothesis
(B) The likelihood of rejecting the null hypothesis when it is true
(C) The probability of detecting an effect when it truly exists
(D) The effect size of the research hypothesis
(C) The probability of detecting an effect when it truly exists
Explanation: The power of a test is the probability of correctly rejecting the null hypothesis when it is false. A higher power increases the likelihood of detecting a true effect when one exists.
78. In hypothesis testing, what does the test statistic represent?
(A) The probability of making a Type II error
(B) The difference between the observed and expected results, measured in standard error units
(C) The level of significance used to reject the null hypothesis
(D) The sample size used in the hypothesis test
(B) The difference between the observed and expected results, measured in standard error units
Explanation: The test statistic measures the difference between the observed results and the expected results under the null hypothesis. It is typically expressed in units of standard error, which allows comparison across different tests.
79. What is the role of random sampling in hypothesis testing?
(A) It ensures that the sample accurately represents the population
(B) It helps reduce the chance of Type I errors
(C) It increases the sample size
(D) It allows for the generalization of the findings
(A) It ensures that the sample accurately represents the population
Explanation: Random sampling ensures that the sample is representative of the population, reducing bias and increasing the likelihood that the results can be generalized to the broader population.
80. Which of the following statements is true about a two-tailed test?
(A) It tests for a relationship in only one direction (positive or negative)
(B) It tests for the possibility of an effect in either direction
(C) It requires a larger sample size than a one-tailed test
(D) It is less powerful than a one-tailed test
(B) It tests for the possibility of an effect in either direction
Explanation: A two-tailed test tests for the possibility of an effect in both directions. It checks whether the effect could be positive or negative, without specifying a direction.
81. What does the confidence interval represent in hypothesis testing?
(A) The range within which the null hypothesis is true
(B) The probability of making a Type II error
(C) The range of values for the sample statistic
(D) The range of values within which the true population parameter is expected to lie with a certain level of confidence
(D) The range of values within which the true population parameter is expected to lie with a certain level of confidence
Explanation: A confidence interval provides a range of values within which the true population parameter is likely to fall, given a certain level of confidence (e.g., 95% confidence level).
82. Which of the following best describes a hypothesis test?
(A) A method used to determine if there is enough evidence to support a specific claim about a population parameter
(B) A process to prove the correctness of a research hypothesis
(C) A way to describe trends and patterns in data
(D) A statistical technique to summarize data
(A) A method used to determine if there is enough evidence to support a specific claim about a population parameter
Explanation: Hypothesis testing is a statistical method used to assess whether there is enough evidence in a sample of data to support a specific claim or hypothesis about a population parameter.
83. Which of the following is an example of a two-tailed test hypothesis?
(A) The average weight of apples is greater than 200 grams
(B) The average weight of apples is equal to 200 grams
(C) The average weight of apples is not equal to 200 grams
(D) The average weight of apples is less than 200 grams
(C) The average weight of apples is not equal to 200 grams
Explanation: A two-tailed test is used to test whether the population parameter (in this case, the average weight) is different from a specific value, in either direction (greater or less). This hypothesis suggests that the average weight of apples is not equal to 200 grams.
84. What does a small p-value indicate in hypothesis testing?
(A) There is strong evidence to support the null hypothesis
(B) There is strong evidence to reject the null hypothesis
(C) The sample size is too small
(D) The hypothesis is not testable
(B) There is strong evidence to reject the null hypothesis
Explanation: A small p-value (typically less than 0.05) indicates that the observed result is unlikely to have occurred by chance, providing strong evidence to reject the null hypothesis in favor of the alternative hypothesis.
85. Which of the following can increase the power of a hypothesis test?
(A) Decreasing the sample size
(B) Increasing the effect size
(C) Decreasing the significance level (α)
(D) Using a less sensitive test
(B) Increasing the effect size
Explanation: Increasing the effect size (the magnitude of the relationship or difference being tested) increases the power of the test. Larger effect sizes are easier to detect, thus increasing the likelihood of rejecting the null hypothesis when it is false.
86. What is the critical region in hypothesis testing?
(A) The range of values where the test statistic is unlikely to fall
(B) The range of values where the null hypothesis is accepted
(C) The range of values where the test statistic would lead to rejecting the null hypothesis
(D) The range of values where the p-value is larger than α
(C) The range of values where the test statistic would lead to rejecting the null hypothesis
Explanation: The critical region (or rejection region) is the range of values for the test statistic that would lead to rejecting the null hypothesis. If the test statistic falls within this region, the null hypothesis is rejected.
87. What is the primary goal of hypothesis testing?
(A) To prove the research hypothesis is true
(B) To reject the null hypothesis if it is false
(C) To test if the data supports the null hypothesis
(D) To determine the significance of the results
(D) To determine the significance of the results
Explanation: The primary goal of hypothesis testing is to determine whether there is sufficient evidence to reject the null hypothesis, which informs the significance of the observed results in relation to the research hypothesis.
88. Which of the following is a characteristic of a good hypothesis?
(A) It should be too broad to test in a single study
(B) It should be based on past research and be testable
(C) It should not require any statistical testing
(D) It should be easily proven true
(B) It should be based on past research and be testable
Explanation: A good hypothesis is grounded in previous research, existing theories, or observations and is testable through experiments or data analysis. It must be specific, measurable, and falsifiable.
89. What is the meaning of falsifiability in the context of a hypothesis?
(A) The hypothesis can be proven true
(B) The hypothesis is based on prior knowledge
(C) The hypothesis can be confirmed through a large sample size
(D) The hypothesis can be tested and potentially shown to be false
(D) The hypothesis can be tested and potentially shown to be false
Explanation: Falsifiability refers to the idea that a hypothesis must be testable and capable of being proven false. This allows for objective testing and validation of hypotheses through experimentation or data analysis.
90. In hypothesis testing, what happens if the null hypothesis is not rejected?
(A) It is proven to be true
(B) It is accepted as true
(C) It is assumed to be false
(D) No conclusion can be made
(B) It is accepted as true
Explanation: If the null hypothesis is not rejected, it means there is insufficient evidence to support the alternative hypothesis. The null hypothesis is considered plausible, but not necessarily proven to be true. It is accepted by default until further evidence suggests otherwise.
91. Which of the following is NOT a step in the hypothesis testing process?
(A) Formulating the research hypothesis
(B) Collecting data and calculating the test statistic
(C) Determining the sample size based on effect size
(D) Repeating the hypothesis testing process until a desired outcome is achieved
(D) Repeating the hypothesis testing process until a desired outcome is achieved
Explanation: The hypothesis testing process is a methodical procedure. Repeating it until a desired outcome is achieved is not a valid step, as it introduces bias. The process involves formulating the hypothesis, collecting data, calculating the test statistic, and then making a decision based on the p-value.
92. In hypothesis testing, what is a Type I error?
(A) Failing to reject the null hypothesis when it is false
(B) Accepting the null hypothesis when it is false
(C) Rejecting the null hypothesis when it is true
(D) Making a conclusion based on incorrect data
(C) Rejecting the null hypothesis when it is true
Explanation: A Type I error occurs when the null hypothesis is rejected even though it is actually true. This is also known as a "false positive" and is related to the level of significance (α).
93. Which of the following is the primary purpose of the null hypothesis in hypothesis testing?
(A) To test the alternative hypothesis
(B) To serve as a baseline for comparison against the alternative hypothesis
(C) To define the range of possible values for the test statistic
(D) To predict the expected result of an experiment
(B) To serve as a baseline for comparison against the alternative hypothesis
Explanation: The null hypothesis serves as the default assumption that there is no effect or relationship between the variables. It is tested against the alternative hypothesis, and the goal is to see if the data provides enough evidence to reject it.
94. What does the power of a test depend on?
(A) Sample size
(B) Significance level (α)
(C) Effect size
(D) All of the above
(D) All of the above
Explanation: The power of a hypothesis test is influenced by several factors, including the sample size, the significance level (α), and the effect size. Larger sample sizes and higher effect sizes generally increase the power of a test.
95. What happens when the confidence interval includes zero?
(A) The null hypothesis is rejected
(B) The test statistic is significant
(C) There is no significant difference or effect
(D) The alternative hypothesis is accepted
(C) There is no significant difference or effect
Explanation: If a confidence interval includes zero, it suggests that there is no significant difference or effect between the two groups being tested, as zero represents the possibility of no difference or no effect.
96. What is one of the primary assumptions of hypothesis testing?
(A) The population is always normally distributed
(B) The sample size must be greater than 100
(C) The data is independent and randomly selected
(D) The alternative hypothesis is always true
(C) The data is independent and randomly selected
Explanation: One of the primary assumptions in hypothesis testing is that the data is independent and randomly selected. This assumption ensures that the results are generalizable and unbiased.
97. If a hypothesis test yields a p-value of 0.04 and the significance level is α = 0.05, what should the researcher do?
(A) Fail to reject the null hypothesis
(B) Accept the null hypothesis
(C) Reject the null hypothesis
(D) Conduct a new test with a larger sample size
(C) Reject the null hypothesis
Explanation: Since the p-value (0.04) is smaller than the significance level (0.05), the researcher should reject the null hypothesis. This indicates that there is significant evidence to support the alternative hypothesis.
98. In hypothesis testing, what does a large effect size indicate?
(A) There is little difference between the groups
(B) The difference between the groups is significant
(C) The null hypothesis should be rejected
(D) The sample size is too small
(B) The difference between the groups is significant
Explanation: A large effect size indicates a substantial difference between the groups being compared, suggesting that the observed effect is likely to be real and not due to random chance.
99. What is the purpose of a two-tailed hypothesis test?
(A) To test whether a population parameter is greater than a specific value
(B) To test whether a population parameter is less than a specific value
(C) To test whether a population parameter is different from a specific value, in either direction
(D) To test for an association between two variables
(C) To test whether a population parameter is different from a specific value, in either direction
Explanation: A two-tailed test is used to test whether a population parameter is significantly different from a specific value, either higher or lower. This test does not specify the direction of the difference.
100. What is a one-tailed hypothesis test used for?
(A) To test for a difference in both directions
(B) To test for a difference in one specific direction (greater or smaller)
(C) To compare multiple groups
(D) To test if the sample mean is equal to the population mean
(B) To test for a difference in one specific direction (greater or smaller)
Explanation: A one-tailed test is used when the researcher predicts a specific direction of the effect (either greater than or smaller than a specified value). It only tests for that direction, not for differences in both directions.
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