SOPHIA STATISTICS UNIT 5 MILESTONE 2026/2027 | Attempt
Score 16/24 | Summer Updated | Complete Q&A | Pass
Guaranteed - A+ Graded
[Section 1: Hypothesis Testing Review & Decision Making (Q1-10)]
Q1. A pharmaceutical company tests a new drug and rejects the null hypothesis that the
drug has no effect when, in reality, the drug truly has no effect. This scenario describes:
A. A correct decision
B. A Type II error
C. A Type I error [CORRECT]
D. A test with high power
Rationale: A Type I error occurs when we reject a true null hypothesis (false positive). A
Type II error (B) is failing to reject a false null. Power (D) is the probability of correctly
rejecting a false null, which did not occur here.
"Correct Answer: C"
Q2. The power of a hypothesis test is defined as:
A. The probability of committing a Type I error
B. The probability of failing to reject a false null hypothesis
C. The probability of correctly rejecting a false null hypothesis [CORRECT]
D. The significance level α multiplied by the sample size
Rationale: Power = 1 − β, where β is the probability of a Type II error. It represents the
probability of detecting an effect when one truly exists. Option A defines α, option B
defines β, and option D is a meaningless calculation.
"Correct Answer: C"
,Q3. Which of the following changes would increase the power of a hypothesis test,
assuming all other factors remain constant?
A. Decreasing the sample size
B. Decreasing the effect size
C. Increasing the sample size [CORRECT]
D. Decreasing the significance level α
Rationale: Increasing sample size (C) decreases standard error, making it easier to
detect true effects. Decreasing n (A) or effect size (B) reduces power. Decreasing α (D)
makes the test more conservative, reducing power.
"Correct Answer: C"
Q4. A 95% confidence interval for a population mean does not contain the null
hypothesis value of 50. At α = 0.05, what is the correct conclusion for a two-tailed
hypothesis test of H₀: μ = 50?
A. Fail to reject H₀ because the interval is wide
B. Reject H₀ because the interval does not contain 50 [CORRECT]
C. Fail to reject H₀ because the confidence level equals 1 − α
D. Reject H₀ only if the sample mean is greater than 50
Rationale: For a two-tailed test at α, reject H₀ if the (1−α)×100% confidence interval
excludes the null value. A 95% CI excluding 50 corresponds to p < 0.05. The width of the
interval (A) and the direction of the mean (D) are irrelevant to this decision rule.
"Correct Answer: B"
Q5. A researcher wants to test whether a new teaching method increases test scores
compared to the traditional method. The appropriate alternative hypothesis is:
A. H₁: μ_new ≠ μ_traditional
B. H₁: μ_new < μ_traditional
C. H₁: μ_new > μ_traditional [CORRECT]
D. H₁: μ_new = μ_traditional
, Rationale: The research question specifies a directional increase, requiring a one-tailed
(right-tailed) alternative. Option A is two-tailed, B is the wrong direction, and D is a null
hypothesis, not an alternative.
"Correct Answer: C"
Q6. A study reports p = 0.03. Which interpretation is correct?
A. There is a 3% probability that the null hypothesis is true
B. There is a 3% probability of obtaining the observed data or more extreme data if the
null hypothesis is true [CORRECT]
C. There is a 97% probability that the alternative hypothesis is true
D. The effect size is large because the p-value is small
Rationale: The p-value is the probability of observing data as or more extreme than the
sample result, assuming H₀ is true. It is not the probability that H₀ (A) or H₁ (C) is true,
nor does it measure effect size (D).
"Correct Answer: B"
Q7. A study with n = 50,000 finds a statistically significant correlation of r = 0.04
between coffee consumption and shoe size (p = 0.02). What is the most appropriate
conclusion?
A. Coffee consumption causes larger shoe size
B. The result is practically meaningless despite statistical significance [CORRECT]
C. The effect size is large because the p-value is significant
D. The sample size is too small to draw conclusions
Rationale: With very large samples, trivial effects can achieve statistical significance. r =
0.04 explains only 0.16% of variance (r² = 0.0016), making it practically meaningless.
Correlation does not imply causation (A), and the sample size is enormous (D).
"Correct Answer: B"
Q8. In hypothesis testing, the significance level α represents:
A. The probability of correctly rejecting H₀
B. The maximum tolerable probability of a Type I error [CORRECT]
C. The probability of a Type II error
Score 16/24 | Summer Updated | Complete Q&A | Pass
Guaranteed - A+ Graded
[Section 1: Hypothesis Testing Review & Decision Making (Q1-10)]
Q1. A pharmaceutical company tests a new drug and rejects the null hypothesis that the
drug has no effect when, in reality, the drug truly has no effect. This scenario describes:
A. A correct decision
B. A Type II error
C. A Type I error [CORRECT]
D. A test with high power
Rationale: A Type I error occurs when we reject a true null hypothesis (false positive). A
Type II error (B) is failing to reject a false null. Power (D) is the probability of correctly
rejecting a false null, which did not occur here.
"Correct Answer: C"
Q2. The power of a hypothesis test is defined as:
A. The probability of committing a Type I error
B. The probability of failing to reject a false null hypothesis
C. The probability of correctly rejecting a false null hypothesis [CORRECT]
D. The significance level α multiplied by the sample size
Rationale: Power = 1 − β, where β is the probability of a Type II error. It represents the
probability of detecting an effect when one truly exists. Option A defines α, option B
defines β, and option D is a meaningless calculation.
"Correct Answer: C"
,Q3. Which of the following changes would increase the power of a hypothesis test,
assuming all other factors remain constant?
A. Decreasing the sample size
B. Decreasing the effect size
C. Increasing the sample size [CORRECT]
D. Decreasing the significance level α
Rationale: Increasing sample size (C) decreases standard error, making it easier to
detect true effects. Decreasing n (A) or effect size (B) reduces power. Decreasing α (D)
makes the test more conservative, reducing power.
"Correct Answer: C"
Q4. A 95% confidence interval for a population mean does not contain the null
hypothesis value of 50. At α = 0.05, what is the correct conclusion for a two-tailed
hypothesis test of H₀: μ = 50?
A. Fail to reject H₀ because the interval is wide
B. Reject H₀ because the interval does not contain 50 [CORRECT]
C. Fail to reject H₀ because the confidence level equals 1 − α
D. Reject H₀ only if the sample mean is greater than 50
Rationale: For a two-tailed test at α, reject H₀ if the (1−α)×100% confidence interval
excludes the null value. A 95% CI excluding 50 corresponds to p < 0.05. The width of the
interval (A) and the direction of the mean (D) are irrelevant to this decision rule.
"Correct Answer: B"
Q5. A researcher wants to test whether a new teaching method increases test scores
compared to the traditional method. The appropriate alternative hypothesis is:
A. H₁: μ_new ≠ μ_traditional
B. H₁: μ_new < μ_traditional
C. H₁: μ_new > μ_traditional [CORRECT]
D. H₁: μ_new = μ_traditional
, Rationale: The research question specifies a directional increase, requiring a one-tailed
(right-tailed) alternative. Option A is two-tailed, B is the wrong direction, and D is a null
hypothesis, not an alternative.
"Correct Answer: C"
Q6. A study reports p = 0.03. Which interpretation is correct?
A. There is a 3% probability that the null hypothesis is true
B. There is a 3% probability of obtaining the observed data or more extreme data if the
null hypothesis is true [CORRECT]
C. There is a 97% probability that the alternative hypothesis is true
D. The effect size is large because the p-value is small
Rationale: The p-value is the probability of observing data as or more extreme than the
sample result, assuming H₀ is true. It is not the probability that H₀ (A) or H₁ (C) is true,
nor does it measure effect size (D).
"Correct Answer: B"
Q7. A study with n = 50,000 finds a statistically significant correlation of r = 0.04
between coffee consumption and shoe size (p = 0.02). What is the most appropriate
conclusion?
A. Coffee consumption causes larger shoe size
B. The result is practically meaningless despite statistical significance [CORRECT]
C. The effect size is large because the p-value is significant
D. The sample size is too small to draw conclusions
Rationale: With very large samples, trivial effects can achieve statistical significance. r =
0.04 explains only 0.16% of variance (r² = 0.0016), making it practically meaningless.
Correlation does not imply causation (A), and the sample size is enormous (D).
"Correct Answer: B"
Q8. In hypothesis testing, the significance level α represents:
A. The probability of correctly rejecting H₀
B. The maximum tolerable probability of a Type I error [CORRECT]
C. The probability of a Type II error
