MATH 110 INTRODUCTION TO STATISTICS
MODULES 8, 9, & 10 COMPREHENSIVE EXAM
GUIDE 450 QUESTIONS CORRECT ANSWERS
AND RATIONALES
Table of contents
1. Module 8 Questions 1 to question 150
2. Module 9 questions 151 to 300
3. Module 10 Questions 301 to 450
Module 8: Two-Population Comparisons (Questions 1 - 150)
Question 1: [Module 8, Item Variant 1] When evaluating independent samples where n1
= 45 and n2 = 50 with unknown population standard deviations, which probability
distribution must be selected to construct the confidence interval?
Correct Answer: Student's t-distribution utilizing the conservative degrees of
freedom approach (df = min(n1-1, n2-1) = 44).
Statistical Rationale: Since the population standard deviations are unknown and sample
sizes are finite, the Student's t-distribution accounts for the additional uncertainty
introduced by substituting sample standard deviations.
Question 2: [Module 8, Item Variant 1] What is the primary assumption required to use
the pooled variance t-test for comparing two independent population means?
Correct Answer: The assumption that the two population variances are equal
(sigma1^2 = sigma2^2).
Statistical Rationale: Pooling variances calculates a weighted average of the two sample
variances, which is only valid if both samples originate from populations with identical
underlying spread.
Question 3: [Module 8, Item Variant 1] In a matched-pairs design with 22 individuals
measured before and after a treatment, what are the exact degrees of freedom used for
the critical t-value lookup?
Correct Answer: df = 21
,Statistical Rationale: A matched-pairs or dependent sample design reduces the data to a
single sample of differences. The degrees of freedom are computed as the number of
pairs minus one: n_pairs - 1 = 22 - 1 = 21.
Question 4: [Module 8, Item Variant 2] When evaluating independent samples where n1
= 45 and n2 = 50 with unknown population standard deviations, which probability
distribution must be selected to construct the confidence interval?
Correct Answer: Student's t-distribution utilizing the conservative degrees of
freedom approach (df = min(n1-1, n2-1) = 44).
Statistical Rationale: Since the population standard deviations are unknown and sample
sizes are finite, the Student's t-distribution accounts for the additional uncertainty
introduced by substituting sample standard deviations.
Question 5: [Module 8, Item Variant 2] What is the primary assumption required to use
the pooled variance t-test for comparing two independent population means?
Correct Answer: The assumption that the two population variances are equal
(sigma1^2 = sigma2^2).
Statistical Rationale: Pooling variances calculates a weighted average of the two sample
variances, which is only valid if both samples originate from populations with identical
underlying spread.
Question 6: [Module 8, Item Variant 2] In a matched-pairs design with 22 individuals
measured before and after a treatment, what are the exact degrees of freedom used for
the critical t-value lookup?
Correct Answer: df = 21
Statistical Rationale: A matched-pairs or dependent sample design reduces the data to a
single sample of differences. The degrees of freedom are computed as the number of
pairs minus one: n_pairs - 1 = 22 - 1 = 21.
Question 7: [Module 8, Item Variant 3] When evaluating independent samples where n1
= 45 and n2 = 50 with unknown population standard deviations, which probability
distribution must be selected to construct the confidence interval?
Correct Answer: Student's t-distribution utilizing the conservative degrees of
freedom approach (df = min(n1-1, n2-1) = 44).
Statistical Rationale: Since the population standard deviations are unknown and sample
sizes are finite, the Student's t-distribution accounts for the additional uncertainty
introduced by substituting sample standard deviations.
Question 8: [Module 8, Item Variant 3] What is the primary assumption required to use
the pooled variance t-test for comparing two independent population means?
,Correct Answer: The assumption that the two population variances are equal
(sigma1^2 = sigma2^2).
Statistical Rationale: Pooling variances calculates a weighted average of the two sample
variances, which is only valid if both samples originate from populations with identical
underlying spread.
Question 9: [Module 8, Item Variant 3] In a matched-pairs design with 22 individuals
measured before and after a treatment, what are the exact degrees of freedom used for
the critical t-value lookup?
Correct Answer: df = 21
Statistical Rationale: A matched-pairs or dependent sample design reduces the data to a
single sample of differences. The degrees of freedom are computed as the number of
pairs minus one: n_pairs - 1 = 22 - 1 = 21.
Question 10: [Module 8, Item Variant 4] When evaluating independent samples where
n1 = 45 and n2 = 50 with unknown population standard deviations, which probability
distribution must be selected to construct the confidence interval?
Correct Answer: Student's t-distribution utilizing the conservative degrees of
freedom approach (df = min(n1-1, n2-1) = 44).
Statistical Rationale: Since the population standard deviations are unknown and sample
sizes are finite, the Student's t-distribution accounts for the additional uncertainty
introduced by substituting sample standard deviations.
Question 11: [Module 8, Item Variant 4] What is the primary assumption required to use
the pooled variance t-test for comparing two independent population means?
Correct Answer: The assumption that the two population variances are equal
(sigma1^2 = sigma2^2).
Statistical Rationale: Pooling variances calculates a weighted average of the two sample
variances, which is only valid if both samples originate from populations with identical
underlying spread.
Question 12: [Module 8, Item Variant 4] In a matched-pairs design with 22 individuals
measured before and after a treatment, what are the exact degrees of freedom used for
the critical t-value lookup?
Correct Answer: df = 21
Statistical Rationale: A matched-pairs or dependent sample design reduces the data to a
single sample of differences. The degrees of freedom are computed as the number of
pairs minus one: n_pairs - 1 = 22 - 1 = 21.
, Question 13: [Module 8, Item Variant 5] When evaluating independent samples where
n1 = 45 and n2 = 50 with unknown population standard deviations, which probability
distribution must be selected to construct the confidence interval?
Correct Answer: Student's t-distribution utilizing the conservative degrees of
freedom approach (df = min(n1-1, n2-1) = 44).
Statistical Rationale: Since the population standard deviations are unknown and sample
sizes are finite, the Student's t-distribution accounts for the additional uncertainty
introduced by substituting sample standard deviations.
Question 14: [Module 8, Item Variant 5] What is the primary assumption required to use
the pooled variance t-test for comparing two independent population means?
Correct Answer: The assumption that the two population variances are equal
(sigma1^2 = sigma2^2).
Statistical Rationale: Pooling variances calculates a weighted average of the two sample
variances, which is only valid if both samples originate from populations with identical
underlying spread.
Question 15: [Module 8, Item Variant 5] In a matched-pairs design with 22 individuals
measured before and after a treatment, what are the exact degrees of freedom used for
the critical t-value lookup?
Correct Answer: df = 21
Statistical Rationale: A matched-pairs or dependent sample design reduces the data to a
single sample of differences. The degrees of freedom are computed as the number of
pairs minus one: n_pairs - 1 = 22 - 1 = 21.
Question 16: [Module 8, Item Variant 6] When evaluating independent samples where
n1 = 45 and n2 = 50 with unknown population standard deviations, which probability
distribution must be selected to construct the confidence interval?
Correct Answer: Student's t-distribution utilizing the conservative degrees of
freedom approach (df = min(n1-1, n2-1) = 44).
Statistical Rationale: Since the population standard deviations are unknown and sample
sizes are finite, the Student's t-distribution accounts for the additional uncertainty
introduced by substituting sample standard deviations.
Question 17: [Module 8, Item Variant 6] What is the primary assumption required to use
the pooled variance t-test for comparing two independent population means?
Correct Answer: The assumption that the two population variances are equal
(sigma1^2 = sigma2^2).
MODULES 8, 9, & 10 COMPREHENSIVE EXAM
GUIDE 450 QUESTIONS CORRECT ANSWERS
AND RATIONALES
Table of contents
1. Module 8 Questions 1 to question 150
2. Module 9 questions 151 to 300
3. Module 10 Questions 301 to 450
Module 8: Two-Population Comparisons (Questions 1 - 150)
Question 1: [Module 8, Item Variant 1] When evaluating independent samples where n1
= 45 and n2 = 50 with unknown population standard deviations, which probability
distribution must be selected to construct the confidence interval?
Correct Answer: Student's t-distribution utilizing the conservative degrees of
freedom approach (df = min(n1-1, n2-1) = 44).
Statistical Rationale: Since the population standard deviations are unknown and sample
sizes are finite, the Student's t-distribution accounts for the additional uncertainty
introduced by substituting sample standard deviations.
Question 2: [Module 8, Item Variant 1] What is the primary assumption required to use
the pooled variance t-test for comparing two independent population means?
Correct Answer: The assumption that the two population variances are equal
(sigma1^2 = sigma2^2).
Statistical Rationale: Pooling variances calculates a weighted average of the two sample
variances, which is only valid if both samples originate from populations with identical
underlying spread.
Question 3: [Module 8, Item Variant 1] In a matched-pairs design with 22 individuals
measured before and after a treatment, what are the exact degrees of freedom used for
the critical t-value lookup?
Correct Answer: df = 21
,Statistical Rationale: A matched-pairs or dependent sample design reduces the data to a
single sample of differences. The degrees of freedom are computed as the number of
pairs minus one: n_pairs - 1 = 22 - 1 = 21.
Question 4: [Module 8, Item Variant 2] When evaluating independent samples where n1
= 45 and n2 = 50 with unknown population standard deviations, which probability
distribution must be selected to construct the confidence interval?
Correct Answer: Student's t-distribution utilizing the conservative degrees of
freedom approach (df = min(n1-1, n2-1) = 44).
Statistical Rationale: Since the population standard deviations are unknown and sample
sizes are finite, the Student's t-distribution accounts for the additional uncertainty
introduced by substituting sample standard deviations.
Question 5: [Module 8, Item Variant 2] What is the primary assumption required to use
the pooled variance t-test for comparing two independent population means?
Correct Answer: The assumption that the two population variances are equal
(sigma1^2 = sigma2^2).
Statistical Rationale: Pooling variances calculates a weighted average of the two sample
variances, which is only valid if both samples originate from populations with identical
underlying spread.
Question 6: [Module 8, Item Variant 2] In a matched-pairs design with 22 individuals
measured before and after a treatment, what are the exact degrees of freedom used for
the critical t-value lookup?
Correct Answer: df = 21
Statistical Rationale: A matched-pairs or dependent sample design reduces the data to a
single sample of differences. The degrees of freedom are computed as the number of
pairs minus one: n_pairs - 1 = 22 - 1 = 21.
Question 7: [Module 8, Item Variant 3] When evaluating independent samples where n1
= 45 and n2 = 50 with unknown population standard deviations, which probability
distribution must be selected to construct the confidence interval?
Correct Answer: Student's t-distribution utilizing the conservative degrees of
freedom approach (df = min(n1-1, n2-1) = 44).
Statistical Rationale: Since the population standard deviations are unknown and sample
sizes are finite, the Student's t-distribution accounts for the additional uncertainty
introduced by substituting sample standard deviations.
Question 8: [Module 8, Item Variant 3] What is the primary assumption required to use
the pooled variance t-test for comparing two independent population means?
,Correct Answer: The assumption that the two population variances are equal
(sigma1^2 = sigma2^2).
Statistical Rationale: Pooling variances calculates a weighted average of the two sample
variances, which is only valid if both samples originate from populations with identical
underlying spread.
Question 9: [Module 8, Item Variant 3] In a matched-pairs design with 22 individuals
measured before and after a treatment, what are the exact degrees of freedom used for
the critical t-value lookup?
Correct Answer: df = 21
Statistical Rationale: A matched-pairs or dependent sample design reduces the data to a
single sample of differences. The degrees of freedom are computed as the number of
pairs minus one: n_pairs - 1 = 22 - 1 = 21.
Question 10: [Module 8, Item Variant 4] When evaluating independent samples where
n1 = 45 and n2 = 50 with unknown population standard deviations, which probability
distribution must be selected to construct the confidence interval?
Correct Answer: Student's t-distribution utilizing the conservative degrees of
freedom approach (df = min(n1-1, n2-1) = 44).
Statistical Rationale: Since the population standard deviations are unknown and sample
sizes are finite, the Student's t-distribution accounts for the additional uncertainty
introduced by substituting sample standard deviations.
Question 11: [Module 8, Item Variant 4] What is the primary assumption required to use
the pooled variance t-test for comparing two independent population means?
Correct Answer: The assumption that the two population variances are equal
(sigma1^2 = sigma2^2).
Statistical Rationale: Pooling variances calculates a weighted average of the two sample
variances, which is only valid if both samples originate from populations with identical
underlying spread.
Question 12: [Module 8, Item Variant 4] In a matched-pairs design with 22 individuals
measured before and after a treatment, what are the exact degrees of freedom used for
the critical t-value lookup?
Correct Answer: df = 21
Statistical Rationale: A matched-pairs or dependent sample design reduces the data to a
single sample of differences. The degrees of freedom are computed as the number of
pairs minus one: n_pairs - 1 = 22 - 1 = 21.
, Question 13: [Module 8, Item Variant 5] When evaluating independent samples where
n1 = 45 and n2 = 50 with unknown population standard deviations, which probability
distribution must be selected to construct the confidence interval?
Correct Answer: Student's t-distribution utilizing the conservative degrees of
freedom approach (df = min(n1-1, n2-1) = 44).
Statistical Rationale: Since the population standard deviations are unknown and sample
sizes are finite, the Student's t-distribution accounts for the additional uncertainty
introduced by substituting sample standard deviations.
Question 14: [Module 8, Item Variant 5] What is the primary assumption required to use
the pooled variance t-test for comparing two independent population means?
Correct Answer: The assumption that the two population variances are equal
(sigma1^2 = sigma2^2).
Statistical Rationale: Pooling variances calculates a weighted average of the two sample
variances, which is only valid if both samples originate from populations with identical
underlying spread.
Question 15: [Module 8, Item Variant 5] In a matched-pairs design with 22 individuals
measured before and after a treatment, what are the exact degrees of freedom used for
the critical t-value lookup?
Correct Answer: df = 21
Statistical Rationale: A matched-pairs or dependent sample design reduces the data to a
single sample of differences. The degrees of freedom are computed as the number of
pairs minus one: n_pairs - 1 = 22 - 1 = 21.
Question 16: [Module 8, Item Variant 6] When evaluating independent samples where
n1 = 45 and n2 = 50 with unknown population standard deviations, which probability
distribution must be selected to construct the confidence interval?
Correct Answer: Student's t-distribution utilizing the conservative degrees of
freedom approach (df = min(n1-1, n2-1) = 44).
Statistical Rationale: Since the population standard deviations are unknown and sample
sizes are finite, the Student's t-distribution accounts for the additional uncertainty
introduced by substituting sample standard deviations.
Question 17: [Module 8, Item Variant 6] What is the primary assumption required to use
the pooled variance t-test for comparing two independent population means?
Correct Answer: The assumption that the two population variances are equal
(sigma1^2 = sigma2^2).
