HSCO 511 FINAL EXAM SCRIPT 2026
QUESTIONS WITH FULL ANSWERS GRADED A+
◉ when the sample size is small (n<30) and σ is known, the correct
distribution to use for a CI for μ is: Answer: standard normal
◉ which action will NOT reduce the margin of error in a one-sample
CI? Answer: increasing σ
◉ the width of a confidence interval for μ decreases as: Answer:
sample size increases
◉ for a one-sample proportion CI, the normal approximation is
appropriate when Answer: np≥ and n(1-p)≥5
◉ A 95% CI for a population proportion uses which critical value?
Answer: z=1.96
◉ Increasing the sample size in a one-sample proportion CI will:
Answer: decrease the width of the CI
◉ A two-sample t-interval for the difference of means requires
which assumption? Answer: independent samples
,◉ when population variances are unknown and assumed equal, the
two-sample interval uses: Answer: pooled variance t-test
◉ the pooled variance estimator is a weighted average of Answer:
the two sample variances
◉ A CI for μ₁ - μ₂ does NOT contain zero. This implies: Answer: a
statistically significant difference exists
◉ Paired analysis is appropriate when Answer: observations are
naturally matched (before/after)
◉ A paired t-interval is constructed using the: Answer: differences
d=x₁ - x₂
◉ The degrees of freedom for a paired t-interval are: Answer: n-1,
where n is the number of pairs
◉ a two-proportion CI for p₁ - p₂ requires which criterion? Answer:
np ≥ 5 and n(1-p) ≥ 5 in each group
◉ Increasing the difference |p̂ ₁ - p̂ ₂| will: Answer: Increase the
magnitude of the point estimate
, ◉ The standard error of p̂ ₁ - p̂ ₂ is smallest when: Answer: Sample
sizes are large
◉ A CI for a single population variance uses: Answer: Chi-square
distribution
◉ A two-sample variance ratio CI uses: Answer: F-distribution
◉ A wider CI for a variance results from: Answer: Having more
dispersion in the data
◉ If a 95% CI for μ is (10.8, 15.2), which statement is correct?
Answer: We are 95% confident the interval contains μ
◉ A confidence interval becomes narrower when: Answer: Sample
size increases
◉ The center of a confidence interval for a proportion is always:
Answer: p̂
◉ Which statement is true regarding CI interpretation? Answer:
Non-overlap of CIs implies significant difference
QUESTIONS WITH FULL ANSWERS GRADED A+
◉ when the sample size is small (n<30) and σ is known, the correct
distribution to use for a CI for μ is: Answer: standard normal
◉ which action will NOT reduce the margin of error in a one-sample
CI? Answer: increasing σ
◉ the width of a confidence interval for μ decreases as: Answer:
sample size increases
◉ for a one-sample proportion CI, the normal approximation is
appropriate when Answer: np≥ and n(1-p)≥5
◉ A 95% CI for a population proportion uses which critical value?
Answer: z=1.96
◉ Increasing the sample size in a one-sample proportion CI will:
Answer: decrease the width of the CI
◉ A two-sample t-interval for the difference of means requires
which assumption? Answer: independent samples
,◉ when population variances are unknown and assumed equal, the
two-sample interval uses: Answer: pooled variance t-test
◉ the pooled variance estimator is a weighted average of Answer:
the two sample variances
◉ A CI for μ₁ - μ₂ does NOT contain zero. This implies: Answer: a
statistically significant difference exists
◉ Paired analysis is appropriate when Answer: observations are
naturally matched (before/after)
◉ A paired t-interval is constructed using the: Answer: differences
d=x₁ - x₂
◉ The degrees of freedom for a paired t-interval are: Answer: n-1,
where n is the number of pairs
◉ a two-proportion CI for p₁ - p₂ requires which criterion? Answer:
np ≥ 5 and n(1-p) ≥ 5 in each group
◉ Increasing the difference |p̂ ₁ - p̂ ₂| will: Answer: Increase the
magnitude of the point estimate
, ◉ The standard error of p̂ ₁ - p̂ ₂ is smallest when: Answer: Sample
sizes are large
◉ A CI for a single population variance uses: Answer: Chi-square
distribution
◉ A two-sample variance ratio CI uses: Answer: F-distribution
◉ A wider CI for a variance results from: Answer: Having more
dispersion in the data
◉ If a 95% CI for μ is (10.8, 15.2), which statement is correct?
Answer: We are 95% confident the interval contains μ
◉ A confidence interval becomes narrower when: Answer: Sample
size increases
◉ The center of a confidence interval for a proportion is always:
Answer: p̂
◉ Which statement is true regarding CI interpretation? Answer:
Non-overlap of CIs implies significant difference
