Statistics Module 3 Exam Actual 2026/2027 –
100% Verified | Detailed Rationales – Pass
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SECTION 1: HYPOTHESIS TESTING FUNDAMENTALS (10 Questions)
Q1. A researcher is testing whether a new teaching method improves student test scores. She sets up
her hypotheses with a significance level of α = 0.05. Which statement correctly describes the null
hypothesis in this context?
A. The new teaching method improves test scores.
B. The new teaching method has no effect on test scores. [CORRECT]
C. The new teaching method worsens test scores.
D. The significance level determines the null hypothesis.
Rationale: The best answer is B. The null hypothesis always represents the status quo or the "no effect"
position—it states that whatever change or intervention you're studying has no impact. In this case, the
null says the teaching method doesn't change test scores. The alternative hypothesis is what the
researcher is actually trying to find evidence for, which would be that the method does improve scores.
Setting α = 0.05 just tells you how much evidence you need to reject that null.
Correct Answer: B
Q2. In a hypothesis test, a Type I error occurs when:
A. You fail to reject the null hypothesis when it is actually false.
B. You reject the null hypothesis when it is actually true. [CORRECT]
C. You reject the alternative hypothesis when it is actually true.
D. You calculate the test statistic incorrectly.
Rationale: The best answer is B. A Type I error is essentially a false positive—you conclude there is an
effect or difference when there really isn't one. This is why we control the probability of Type I error
with our significance level α; we're setting a cap on how often we're willing to make this particular
mistake. A Type II error, by contrast, is failing to detect an effect that is actually there.
,Correct Answer: B
Q3. A pharmaceutical company tests a new drug and reports a p-value of 0.03. Using a significance level
of α = 0.05, which conclusion is most appropriate?
A. The drug is proven to be effective with 97% certainty.
B. There is sufficient evidence to reject the null hypothesis and conclude the drug has a statistically
significant effect. [CORRECT]
C. The probability that the null hypothesis is true is 3%.
D. The drug has no effect because the p-value is greater than 0.01.
Rationale: The best answer is B. When your p-value (0.03) falls below your significance level (0.05), you
have enough evidence to reject the null hypothesis. This means the observed effect is unlikely to have
occurred by random chance alone. However, it's important to remember that the p-value is not the
probability that the null is true, nor is it a measure of how certain we are about the drug's
effectiveness—it's simply the probability of seeing data this extreme if the null were actually true.
Correct Answer: B
Q4. A researcher conducts a study with α = 0.01 instead of the more common α = 0.05. Which
consequence is most likely?
A. The study will have more power to detect true effects.
B. The probability of a Type I error decreases, but the probability of a Type II error increases. [CORRECT]
C. The p-value will automatically be smaller.
D. The sample size requirements will decrease.
Rationale: The best answer is B. Lowering your significance level makes it harder to reject the null
hypothesis, which means you're less likely to make a Type I error (good), but you're also more likely to
miss a real effect when one exists—a Type II error. It's a trade-off. The p-value itself doesn't change
based on your chosen α; it's calculated from the data. And if anything, a more stringent α usually
requires a larger sample size to maintain adequate power, not a smaller one.
Correct Answer: B
Q5. Which of the following best describes the relationship between the test statistic and the p-value in
hypothesis testing?
A. The test statistic and p-value are completely unrelated.
B. A larger absolute test statistic generally corresponds to a smaller p-value, indicating stronger evidence
, against the null hypothesis. [CORRECT]
C. The p-value is always equal to the test statistic divided by the sample size.
D. A smaller test statistic always indicates a smaller p-value.
Rationale: The best answer is B. The test statistic measures how far your sample result is from what the
null hypothesis predicts, standardized by the standard error. The farther your result is from the null
expectation (in either direction), the larger the absolute test statistic, and the less likely that result
would occur by chance. That translates to a smaller p-value. There's no simple division formula that
connects them, and the relationship is inverse, not direct.
Correct Answer: B
Q6. A researcher is deciding between a one-tailed and a two-tailed test. Which consideration is most
important?
A. A one-tailed test is always more appropriate than a two-tailed test.
B. The choice should be based on the research question and whether the direction of the effect is
specified in advance. [CORRECT]
C. A two-tailed test should only be used when the sample size is large.
D. The p-value is always smaller for a two-tailed test.
Rationale: The best answer is B. You choose a one-tailed test when you have a specific directional
prediction before looking at the data—for example, "this drug will increase scores" rather than just "this
drug will change scores." Using a one-tailed test when you don't have a strong directional hypothesis is
considered bad practice because it inflates your chance of a Type I error. The decision should be driven
by your research question, not by sample size or a desire for a smaller p-value.
Correct Answer: B
Q7. In hypothesis testing, the critical value is:
A. The value of the test statistic that corresponds to the p-value.
B. The threshold value that separates the rejection region from the non-rejection region, determined by
the significance level and the test distribution. [CORRECT]
C. Always equal to 1.96 for any test.
D. The same as the sample mean.
Rationale: The best answer is B. The critical value is the cutoff point on your test distribution (like the z-
distribution or t-distribution) that defines the rejection region. If your test statistic falls beyond this
value, you reject the null hypothesis. It's determined by your chosen significance level α and the shape
100% Verified | Detailed Rationales – Pass
Guaranteed – A+ Graded
SECTION 1: HYPOTHESIS TESTING FUNDAMENTALS (10 Questions)
Q1. A researcher is testing whether a new teaching method improves student test scores. She sets up
her hypotheses with a significance level of α = 0.05. Which statement correctly describes the null
hypothesis in this context?
A. The new teaching method improves test scores.
B. The new teaching method has no effect on test scores. [CORRECT]
C. The new teaching method worsens test scores.
D. The significance level determines the null hypothesis.
Rationale: The best answer is B. The null hypothesis always represents the status quo or the "no effect"
position—it states that whatever change or intervention you're studying has no impact. In this case, the
null says the teaching method doesn't change test scores. The alternative hypothesis is what the
researcher is actually trying to find evidence for, which would be that the method does improve scores.
Setting α = 0.05 just tells you how much evidence you need to reject that null.
Correct Answer: B
Q2. In a hypothesis test, a Type I error occurs when:
A. You fail to reject the null hypothesis when it is actually false.
B. You reject the null hypothesis when it is actually true. [CORRECT]
C. You reject the alternative hypothesis when it is actually true.
D. You calculate the test statistic incorrectly.
Rationale: The best answer is B. A Type I error is essentially a false positive—you conclude there is an
effect or difference when there really isn't one. This is why we control the probability of Type I error
with our significance level α; we're setting a cap on how often we're willing to make this particular
mistake. A Type II error, by contrast, is failing to detect an effect that is actually there.
,Correct Answer: B
Q3. A pharmaceutical company tests a new drug and reports a p-value of 0.03. Using a significance level
of α = 0.05, which conclusion is most appropriate?
A. The drug is proven to be effective with 97% certainty.
B. There is sufficient evidence to reject the null hypothesis and conclude the drug has a statistically
significant effect. [CORRECT]
C. The probability that the null hypothesis is true is 3%.
D. The drug has no effect because the p-value is greater than 0.01.
Rationale: The best answer is B. When your p-value (0.03) falls below your significance level (0.05), you
have enough evidence to reject the null hypothesis. This means the observed effect is unlikely to have
occurred by random chance alone. However, it's important to remember that the p-value is not the
probability that the null is true, nor is it a measure of how certain we are about the drug's
effectiveness—it's simply the probability of seeing data this extreme if the null were actually true.
Correct Answer: B
Q4. A researcher conducts a study with α = 0.01 instead of the more common α = 0.05. Which
consequence is most likely?
A. The study will have more power to detect true effects.
B. The probability of a Type I error decreases, but the probability of a Type II error increases. [CORRECT]
C. The p-value will automatically be smaller.
D. The sample size requirements will decrease.
Rationale: The best answer is B. Lowering your significance level makes it harder to reject the null
hypothesis, which means you're less likely to make a Type I error (good), but you're also more likely to
miss a real effect when one exists—a Type II error. It's a trade-off. The p-value itself doesn't change
based on your chosen α; it's calculated from the data. And if anything, a more stringent α usually
requires a larger sample size to maintain adequate power, not a smaller one.
Correct Answer: B
Q5. Which of the following best describes the relationship between the test statistic and the p-value in
hypothesis testing?
A. The test statistic and p-value are completely unrelated.
B. A larger absolute test statistic generally corresponds to a smaller p-value, indicating stronger evidence
, against the null hypothesis. [CORRECT]
C. The p-value is always equal to the test statistic divided by the sample size.
D. A smaller test statistic always indicates a smaller p-value.
Rationale: The best answer is B. The test statistic measures how far your sample result is from what the
null hypothesis predicts, standardized by the standard error. The farther your result is from the null
expectation (in either direction), the larger the absolute test statistic, and the less likely that result
would occur by chance. That translates to a smaller p-value. There's no simple division formula that
connects them, and the relationship is inverse, not direct.
Correct Answer: B
Q6. A researcher is deciding between a one-tailed and a two-tailed test. Which consideration is most
important?
A. A one-tailed test is always more appropriate than a two-tailed test.
B. The choice should be based on the research question and whether the direction of the effect is
specified in advance. [CORRECT]
C. A two-tailed test should only be used when the sample size is large.
D. The p-value is always smaller for a two-tailed test.
Rationale: The best answer is B. You choose a one-tailed test when you have a specific directional
prediction before looking at the data—for example, "this drug will increase scores" rather than just "this
drug will change scores." Using a one-tailed test when you don't have a strong directional hypothesis is
considered bad practice because it inflates your chance of a Type I error. The decision should be driven
by your research question, not by sample size or a desire for a smaller p-value.
Correct Answer: B
Q7. In hypothesis testing, the critical value is:
A. The value of the test statistic that corresponds to the p-value.
B. The threshold value that separates the rejection region from the non-rejection region, determined by
the significance level and the test distribution. [CORRECT]
C. Always equal to 1.96 for any test.
D. The same as the sample mean.
Rationale: The best answer is B. The critical value is the cutoff point on your test distribution (like the z-
distribution or t-distribution) that defines the rejection region. If your test statistic falls beyond this
value, you reject the null hypothesis. It's determined by your chosen significance level α and the shape
