STAT 330 - CHAPTER 9 | GUARANTEED SUCCESS STARTS
HERE! LEARN, PRACTICE & EXCEL!
Q: What is a point estimate? Answer: A single value used to estimate a population parameter.
Q: What is a confidence interval? Answer: An interval estimate that provides a range of
plausible values for a parameter.
Q: What is the general form of a confidence interval? Answer: Estimator ± (critical
value)(standard error).
Q: What is the interpretation of a 95% confidence interval? Answer: If repeated samples are
taken, about 95% of such intervals will contain the true parameter.
Q: What is the standard error of the mean when σ is known? Answer: σ/√n.
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 the CI for μ when σ is unknown? Answer: X̄ ± t(α/2, n-1)(S/√n).
Q: What is the CI for μ when σ is known? Answer: X̄ ± z(α/2)(σ/√n).
Q: What is the CI for a population proportion p? Answer: p̂ ± z(α/2)√[p̂ (1-p̂)/n].
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 difference of means (equal variance)? Answer: (X̄1-X̄2) ± t(α/2, n1+n2-
2)√[Sp²(1/n1+1/n2)].
Q: What is the CI for difference of means (unequal variance)? Answer: (X̄1-X̄ 2) ± 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-p̂ 2) ± z(α/2)√[(p̂ 1(1-
p̂1)/n1)+(p̂2(1-p̂ 2)/n2)].
Q: What is the CI for variance σ²? Answer: ((n-1)S²/χ²(α/2,n-1), (n-1)S²/χ²(1-α/2,n-1)).
Q: What is an unbiased estimator? Answer: An estimator with expected value equal to the
parameter.
Q: What is efficiency of an estimator? Answer: An estimator is efficient if it has smallest
variance among unbiased estimators.
APPHIA – Crafted with Care and Precision for Academic Excellence.
1
HERE! LEARN, PRACTICE & EXCEL!
Q: What is a point estimate? Answer: A single value used to estimate a population parameter.
Q: What is a confidence interval? Answer: An interval estimate that provides a range of
plausible values for a parameter.
Q: What is the general form of a confidence interval? Answer: Estimator ± (critical
value)(standard error).
Q: What is the interpretation of a 95% confidence interval? Answer: If repeated samples are
taken, about 95% of such intervals will contain the true parameter.
Q: What is the standard error of the mean when σ is known? Answer: σ/√n.
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 the CI for μ when σ is unknown? Answer: X̄ ± t(α/2, n-1)(S/√n).
Q: What is the CI for μ when σ is known? Answer: X̄ ± z(α/2)(σ/√n).
Q: What is the CI for a population proportion p? Answer: p̂ ± z(α/2)√[p̂ (1-p̂)/n].
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 difference of means (equal variance)? Answer: (X̄1-X̄2) ± t(α/2, n1+n2-
2)√[Sp²(1/n1+1/n2)].
Q: What is the CI for difference of means (unequal variance)? Answer: (X̄1-X̄ 2) ± 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-p̂ 2) ± z(α/2)√[(p̂ 1(1-
p̂1)/n1)+(p̂2(1-p̂ 2)/n2)].
Q: What is the CI for variance σ²? Answer: ((n-1)S²/χ²(α/2,n-1), (n-1)S²/χ²(1-α/2,n-1)).
Q: What is an unbiased estimator? Answer: An estimator with expected value equal to the
parameter.
Q: What is efficiency of an estimator? Answer: An estimator is efficient if it has smallest
variance among unbiased estimators.
APPHIA – Crafted with Care and Precision for Academic Excellence.
1
