STAT 330 Chapter 9 Solved 100% Correct
Q: Example: Sample of 100 with X̄=50 - ANSWER-σ=10. 95% CI for μ?,50 ±
1.96(10/√100) = (48.04, 51.96).
Q: Example: Two independent samples with equal variances. Which test is used? -
ANSWER-Pooled two-sample t-test.
Q: What distribution is used for CI of mean when σ is known? - ANSWER-Normal
distribution.
Q: What distribution is used for CI of mean when σ is unknown? - ANSWER-t-
distribution with n-1 degrees of freedom.
Q: What is a confidence interval? - ANSWER-An interval estimate that provides a range
of plausible values for a parameter.
Q: What is a point estimate? - ANSWER-A single value used to estimate a population
parameter.
Q: What is an unbiased estimator? - ANSWER-An estimator with expected value equal
to the parameter.
Q: What is consistency of an estimator? - ANSWER-An estimator is consistent if it
converges in probability to the true parameter as n→∞.
Q: What is efficiency of an estimator? - ANSWER-An estimator is efficient if it has
smallest variance among unbiased estimators.
Q: What is maximum likelihood estimation (MLE)? - ANSWER-A method of estimating
parameters by maximizing the likelihood function.
Q: What is pooled variance in two-sample t-tests? - ANSWER-Sp² = [(n1-1)S1² + (n2-
1)S2²] / (n1+n2-2).
Q: What is the CI for a population proportion p? - ANSWER-p̂ ± z(α/2)√[p̂(1-p̂)/n].
Q: What is the CI for difference of means (equal variance)? - ANSWER-(X̄ 1-X̄2) ± t(α/2,
n1+n2-2)√[Sp²(1/n1+1/n2)].
Q: What is the CI for difference of means (unequal variance)? - ANSWER-(X̄ 1-X̄2) ±
t(α/2, df)√[(S1²/n1)+(S2²/n2)], Welch's formula for df.
Q: What is the CI for the difference in two proportions? - ANSWER-(p̂1-p̂2) ±
z(α/2)√[(p̂1(1-p̂1)/n1)+(p̂2(1-p̂2)/n2)].
Q: Example: Sample of 100 with X̄=50 - ANSWER-σ=10. 95% CI for μ?,50 ±
1.96(10/√100) = (48.04, 51.96).
Q: Example: Two independent samples with equal variances. Which test is used? -
ANSWER-Pooled two-sample t-test.
Q: What distribution is used for CI of mean when σ is known? - ANSWER-Normal
distribution.
Q: What distribution is used for CI of mean when σ is unknown? - ANSWER-t-
distribution with n-1 degrees of freedom.
Q: What is a confidence interval? - ANSWER-An interval estimate that provides a range
of plausible values for a parameter.
Q: What is a point estimate? - ANSWER-A single value used to estimate a population
parameter.
Q: What is an unbiased estimator? - ANSWER-An estimator with expected value equal
to the parameter.
Q: What is consistency of an estimator? - ANSWER-An estimator is consistent if it
converges in probability to the true parameter as n→∞.
Q: What is efficiency of an estimator? - ANSWER-An estimator is efficient if it has
smallest variance among unbiased estimators.
Q: What is maximum likelihood estimation (MLE)? - ANSWER-A method of estimating
parameters by maximizing the likelihood function.
Q: What is pooled variance in two-sample t-tests? - ANSWER-Sp² = [(n1-1)S1² + (n2-
1)S2²] / (n1+n2-2).
Q: What is the CI for a population proportion p? - ANSWER-p̂ ± z(α/2)√[p̂(1-p̂)/n].
Q: What is the CI for difference of means (equal variance)? - ANSWER-(X̄ 1-X̄2) ± t(α/2,
n1+n2-2)√[Sp²(1/n1+1/n2)].
Q: What is the CI for difference of means (unequal variance)? - ANSWER-(X̄ 1-X̄2) ±
t(α/2, df)√[(S1²/n1)+(S2²/n2)], Welch's formula for df.
Q: What is the CI for the difference in two proportions? - ANSWER-(p̂1-p̂2) ±
z(α/2)√[(p̂1(1-p̂1)/n1)+(p̂2(1-p̂2)/n2)].
