HSCO 511 FINAL PRACTICE SOLUTION 2026
QUESTIONS WITH COMPLETE ANSWERS
GRADED A+
◉ 2. When the sample size is small (n < 30) and σ is known, the
correct distribution to use for a CI for μ is:
a) Standard normal
b) Student t with n-1 df
c) Chi-square
d) F-ratio. Answer: a) Standard normal
◉ 3. Which action will not reduce the margin of error in a one-
sample mean CI?
a) Increasing n
b) Decreasing the confidence level
c) Decreasing σ
d) Increasing σ. Answer: d) Increasing σ
◉ 4. The width of a confidence interval for μ decreases as:
a) Confidence level increases
b) Sample size increases
c) Standard deviation increases
,d) t-critical value increases. Answer: b) Sample size increases
◉ 5. For a one-sample proportion CI, the normal approximation is
appropriate when:
a) np ≥ 5 and n(1-p) ≥ 5
b) n ≥ 10
c) The population is normal
d) Large n and small p. Answer: a) np ≥ 5 and n(1-p) ≥ 5
◉ 6. A 95% CI for a population proportion uses which critical value?
a) t{0.025, n-1}
b) z = 1.96
c) z = 1.645
d) F{0.025}. Answer: b) z = 1.96
◉ 7. Increasing the sample size in a one-sample proportion CI will:
a) Increase bias
b) Decrease the width of the CI
c) Increase the variability of p̂
d) Change the point estimate p̂ . Answer: b) Decrease the width of the
CI
,◉ 8. A two-sample t-interval for the difference of means requires
which assumption?
a) Both populations must be normally distributed regardless of n
b) Equal sample sizes
c) Independent samples
d) σ₁ = σ₂ always. Answer: c) Independent samples
◉ 9. When population variances are assumed equal, the two-sample
interval uses:
a) Separate variances t-test
b) Pooled variance t-test
c) Z-interval
d) Welch-Satterthwaite variance t-test. Answer: b) Pooled variance t-
test
◉ 10. The pooled variance estimator is a weighted average of:
a) The two sample means
b) The two sample variances
c) The standard errors for each group
d) The t-critical values. Answer: b) The two sample variances
◉ 11. A CI for μ₁ - μ₂ does not contain zero. This implies:
, a) Means are equal
b) A statistically significant difference exists
c) Both sample means are large
d) Variances differ significantly. Answer: b) A statistically significant
difference exists
◉ 12. Paired analysis is appropriate when:
a) Samples are independent
b) Subjects are randomly assigned to separate groups
c) Observations are naturally matched (e.g., before/after)
d) The variances are unequal. Answer: c) Observations are naturally
matched (e.g., before/after)
◉ 13. A paired t-interval is constructed using the:
a) Differences d = x₁ - x₂
b) Pooled variance of both groups
c) Larger sample's variance
d) Standard normal distribution. Answer: a) Differences d = x₁ - x₂
◉ 14. The degrees of freedom for a paired t-interval are:
a) n₁ + n₂ - 2
b) n - 1, where n is the number of pairs
QUESTIONS WITH COMPLETE ANSWERS
GRADED A+
◉ 2. When the sample size is small (n < 30) and σ is known, the
correct distribution to use for a CI for μ is:
a) Standard normal
b) Student t with n-1 df
c) Chi-square
d) F-ratio. Answer: a) Standard normal
◉ 3. Which action will not reduce the margin of error in a one-
sample mean CI?
a) Increasing n
b) Decreasing the confidence level
c) Decreasing σ
d) Increasing σ. Answer: d) Increasing σ
◉ 4. The width of a confidence interval for μ decreases as:
a) Confidence level increases
b) Sample size increases
c) Standard deviation increases
,d) t-critical value increases. Answer: b) Sample size increases
◉ 5. For a one-sample proportion CI, the normal approximation is
appropriate when:
a) np ≥ 5 and n(1-p) ≥ 5
b) n ≥ 10
c) The population is normal
d) Large n and small p. Answer: a) np ≥ 5 and n(1-p) ≥ 5
◉ 6. A 95% CI for a population proportion uses which critical value?
a) t{0.025, n-1}
b) z = 1.96
c) z = 1.645
d) F{0.025}. Answer: b) z = 1.96
◉ 7. Increasing the sample size in a one-sample proportion CI will:
a) Increase bias
b) Decrease the width of the CI
c) Increase the variability of p̂
d) Change the point estimate p̂ . Answer: b) Decrease the width of the
CI
,◉ 8. A two-sample t-interval for the difference of means requires
which assumption?
a) Both populations must be normally distributed regardless of n
b) Equal sample sizes
c) Independent samples
d) σ₁ = σ₂ always. Answer: c) Independent samples
◉ 9. When population variances are assumed equal, the two-sample
interval uses:
a) Separate variances t-test
b) Pooled variance t-test
c) Z-interval
d) Welch-Satterthwaite variance t-test. Answer: b) Pooled variance t-
test
◉ 10. The pooled variance estimator is a weighted average of:
a) The two sample means
b) The two sample variances
c) The standard errors for each group
d) The t-critical values. Answer: b) The two sample variances
◉ 11. A CI for μ₁ - μ₂ does not contain zero. This implies:
, a) Means are equal
b) A statistically significant difference exists
c) Both sample means are large
d) Variances differ significantly. Answer: b) A statistically significant
difference exists
◉ 12. Paired analysis is appropriate when:
a) Samples are independent
b) Subjects are randomly assigned to separate groups
c) Observations are naturally matched (e.g., before/after)
d) The variances are unequal. Answer: c) Observations are naturally
matched (e.g., before/after)
◉ 13. A paired t-interval is constructed using the:
a) Differences d = x₁ - x₂
b) Pooled variance of both groups
c) Larger sample's variance
d) Standard normal distribution. Answer: a) Differences d = x₁ - x₂
◉ 14. The degrees of freedom for a paired t-interval are:
a) n₁ + n₂ - 2
b) n - 1, where n is the number of pairs
