STAT 330 - Chapter 9
Q: Example: Sample of 100 with X̄=50 σ=10. 95% CI for μ?,50 ± 1.96(10/√100) = (48.04, 51.96).
Q: Example: Two independent samples with equal variances. Pooled two-sample t-test.
Which test is used?
Q: What distribution is used for CI of mean when σ is known? Normal distribution.
Q: What distribution is used for CI of mean when σ is t-distribution with n-1 degrees of freedom.
unknown?
Q: What is a confidence interval? An interval estimate that provides a range of plausible values for a parameter.
Q: What is an unbiased estimator? An estimator with expected value equal to the parameter.
Q: What is a point estimate? A single value used to estimate a population parameter.
Q: What is consistency of an estimator? An estimator is consistent if it converges in probability to the true parameter as n→∞.
Q: What is efficiency of an estimator? An estimator is efficient if it has smallest variance among unbiased estimators.
Q: What is maximum likelihood estimation (MLE)? A method of estimating parameters by maximizing the likelihood function.
Q: What is pooled variance in two-sample t-tests? Sp² = [(n1-1)S1² + (n2-1)S2²] / (n1+n2-2).
Q: What is the CI for a population proportion p? p̂ ± z(α/2)√[p̂(1-p̂)/n].
Q: What is the CI for difference of means (equal variance)? (X̄1-X̄2) ± t(α/2, n1+n2-2)√[Sp²(1/n1+1/n2)].
Q: What is the CI for difference of means (unequal variance)? (X̄1-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? (p̂1-p̂2) ± z(α/2)√[(p̂1(1-p̂1)/n1)+(p̂2(1-p̂2)/n2)].
Q: What is the CI for variance σ²? ((n-1)S²/χ²(α/2,n-1), (n-1)S²/χ²(1-α/2,n-1)).
Q: What is the CI for μ when σ is known? X̄ ± z(α/2)(σ/√n).
Q: What is the CI for μ when σ is unknown? X̄ ± t(α/2, n-1)(S/√n).
Q: What is the general form of a confidence interval? Estimator ± (critical value)(standard error).
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Q: Example: Sample of 100 with X̄=50 σ=10. 95% CI for μ?,50 ± 1.96(10/√100) = (48.04, 51.96).
Q: Example: Two independent samples with equal variances. Pooled two-sample t-test.
Which test is used?
Q: What distribution is used for CI of mean when σ is known? Normal distribution.
Q: What distribution is used for CI of mean when σ is t-distribution with n-1 degrees of freedom.
unknown?
Q: What is a confidence interval? An interval estimate that provides a range of plausible values for a parameter.
Q: What is an unbiased estimator? An estimator with expected value equal to the parameter.
Q: What is a point estimate? A single value used to estimate a population parameter.
Q: What is consistency of an estimator? An estimator is consistent if it converges in probability to the true parameter as n→∞.
Q: What is efficiency of an estimator? An estimator is efficient if it has smallest variance among unbiased estimators.
Q: What is maximum likelihood estimation (MLE)? A method of estimating parameters by maximizing the likelihood function.
Q: What is pooled variance in two-sample t-tests? Sp² = [(n1-1)S1² + (n2-1)S2²] / (n1+n2-2).
Q: What is the CI for a population proportion p? p̂ ± z(α/2)√[p̂(1-p̂)/n].
Q: What is the CI for difference of means (equal variance)? (X̄1-X̄2) ± t(α/2, n1+n2-2)√[Sp²(1/n1+1/n2)].
Q: What is the CI for difference of means (unequal variance)? (X̄1-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? (p̂1-p̂2) ± z(α/2)√[(p̂1(1-p̂1)/n1)+(p̂2(1-p̂2)/n2)].
Q: What is the CI for variance σ²? ((n-1)S²/χ²(α/2,n-1), (n-1)S²/χ²(1-α/2,n-1)).
Q: What is the CI for μ when σ is known? X̄ ± z(α/2)(σ/√n).
Q: What is the CI for μ when σ is unknown? X̄ ± t(α/2, n-1)(S/√n).
Q: What is the general form of a confidence interval? Estimator ± (critical value)(standard error).
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