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MATH 110 Module 6 Actual Exam
2026/2027: Scored 100% - Portage
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Section 1: Hypothesis Testing Fundamentals (4 Questions)
Q1: A researcher wants to test whether a new teaching method increases student test scores. The
null hypothesis states that the mean score is 75, while the alternative hypothesis states that the
mean is greater than 75. What type of test is this?
• A. Two-tailed test
• B. Left-tailed test
• C. Right-tailed (one-tailed) test [CORRECT]
• D. Non-directional test
Correct Answer: C Rationale: This is a right-tailed (one-tailed) test because the alternative
hypothesis (Hₐ: μ > 75) specifies a direction—specifically that the mean is greater than the
hypothesized value. The rejection region is entirely in the right tail of the distribution. Option A
is incorrect because a two-tailed test would test for difference in either direction (μ ≠ 75). Option
B is incorrect because that would test if the mean is less than 75. Option D is synonymous with a
two-tailed test.
Q2: In hypothesis testing, the p-value represents:
• A. The probability that the null hypothesis is true
• B. The probability of obtaining a test statistic at least as extreme as the one observed,
assuming the null hypothesis is true [CORRECT]
• C. The probability of making a Type II error
• D. The significance level α chosen by the researcher
Correct Answer: B Rationale: The p-value is the probability of obtaining sample results at least
as extreme as those observed, given that the null hypothesis is true. It is NOT the probability that
H₀ is true (a common misconception in Option A). Option C describes β (beta), the probability of
, 2
Type II error. Option D describes α (alpha), the significance level threshold for decision-making,
not the calculated p-value.
Q3: A study reports a test statistic of z = 2.15 with a corresponding p-value of 0.0158. Using α =
0.05, what is the appropriate conclusion?
• A. Fail to reject H₀; there is insufficient evidence to support the claim
• B. Reject H₀; there is sufficient evidence to support the alternative hypothesis
[CORRECT]
• C. Accept H₀ as true
• D. The results are inconclusive
Correct Answer: B Rationale: Since the p-value (0.0158) is less than the significance level (α =
0.05), we reject the null hypothesis. This indicates sufficient statistical evidence to support the
alternative hypothesis. Option A is incorrect because the p-value is less than α, not greater.
Option C is incorrect because we never "accept" H₀—we either reject it or fail to reject it. Option
D is incorrect because the decision is clear when p-value < α.
Q4: Which of the following statements best describes the relationship between statistical
significance and practical significance?
• A. They are always equivalent; if a result is statistically significant, it is always
practically important
• B. Statistical significance indicates the result is unlikely due to chance, while practical
significance indicates the result is meaningful in real-world context [CORRECT]
• C. Practical significance is determined by the p-value, while statistical significance is
determined by effect size
• D. A large sample size ensures both statistical and practical significance
Correct Answer: B Rationale: Statistical significance (determined by p-value < α) indicates the
observed effect is unlikely due to random sampling alone. Practical significance considers
whether the effect size is large enough to matter in real-world applications. With very large
samples, tiny effects can be statistically significant but practically meaningless. Option A is
incorrect because these concepts differ. Option C reverses the definitions. Option D is incorrect
because large samples can detect trivial effects that lack practical importance.
Section 2: One-Sample Tests (5 Questions)
MATH 110 Module 6 Actual Exam
2026/2027: Scored 100% - Portage
Learning for Statistics Success – Pass
Guaranteed - A+ Graded
Section 1: Hypothesis Testing Fundamentals (4 Questions)
Q1: A researcher wants to test whether a new teaching method increases student test scores. The
null hypothesis states that the mean score is 75, while the alternative hypothesis states that the
mean is greater than 75. What type of test is this?
• A. Two-tailed test
• B. Left-tailed test
• C. Right-tailed (one-tailed) test [CORRECT]
• D. Non-directional test
Correct Answer: C Rationale: This is a right-tailed (one-tailed) test because the alternative
hypothesis (Hₐ: μ > 75) specifies a direction—specifically that the mean is greater than the
hypothesized value. The rejection region is entirely in the right tail of the distribution. Option A
is incorrect because a two-tailed test would test for difference in either direction (μ ≠ 75). Option
B is incorrect because that would test if the mean is less than 75. Option D is synonymous with a
two-tailed test.
Q2: In hypothesis testing, the p-value represents:
• A. The probability that the null hypothesis is true
• B. The probability of obtaining a test statistic at least as extreme as the one observed,
assuming the null hypothesis is true [CORRECT]
• C. The probability of making a Type II error
• D. The significance level α chosen by the researcher
Correct Answer: B Rationale: The p-value is the probability of obtaining sample results at least
as extreme as those observed, given that the null hypothesis is true. It is NOT the probability that
H₀ is true (a common misconception in Option A). Option C describes β (beta), the probability of
, 2
Type II error. Option D describes α (alpha), the significance level threshold for decision-making,
not the calculated p-value.
Q3: A study reports a test statistic of z = 2.15 with a corresponding p-value of 0.0158. Using α =
0.05, what is the appropriate conclusion?
• A. Fail to reject H₀; there is insufficient evidence to support the claim
• B. Reject H₀; there is sufficient evidence to support the alternative hypothesis
[CORRECT]
• C. Accept H₀ as true
• D. The results are inconclusive
Correct Answer: B Rationale: Since the p-value (0.0158) is less than the significance level (α =
0.05), we reject the null hypothesis. This indicates sufficient statistical evidence to support the
alternative hypothesis. Option A is incorrect because the p-value is less than α, not greater.
Option C is incorrect because we never "accept" H₀—we either reject it or fail to reject it. Option
D is incorrect because the decision is clear when p-value < α.
Q4: Which of the following statements best describes the relationship between statistical
significance and practical significance?
• A. They are always equivalent; if a result is statistically significant, it is always
practically important
• B. Statistical significance indicates the result is unlikely due to chance, while practical
significance indicates the result is meaningful in real-world context [CORRECT]
• C. Practical significance is determined by the p-value, while statistical significance is
determined by effect size
• D. A large sample size ensures both statistical and practical significance
Correct Answer: B Rationale: Statistical significance (determined by p-value < α) indicates the
observed effect is unlikely due to random sampling alone. Practical significance considers
whether the effect size is large enough to matter in real-world applications. With very large
samples, tiny effects can be statistically significant but practically meaningless. Option A is
incorrect because these concepts differ. Option C reverses the definitions. Option D is incorrect
because large samples can detect trivial effects that lack practical importance.
Section 2: One-Sample Tests (5 Questions)
