Let Y be a random variable. Suppose you are interested in estimating the populat

Question

Let Y be a random variable. Suppose you are interested in estimating the population mean, E(Y). Which of the following statements about confidence intervals and hypotheses tests are true? (Check all that apply.) A confidence interval defines a rejection rule, at a specified significance level, for all possible values of the population mean, E(Y), whereas a single hypothesis test is a rejection rule for only one possible value of the population mean. A confidence interval defines a rejection rule, at a specified significance level, for only one possible value of the population mean, E(Y), whereas a single hypothesis test is a rejection rule for all possible values of the population mean. A confidence interval summarizes the set of hypotheses about the population mean, E(Y), you can and cannot reject at a given significance level. A single hypothesis test about the population mean, E(Y), contains more information than a confidence interval.

Explanation / Answer

Solution:-

a) A confidence interval defines a rejection rule, at a specified significance level, for all possible values of the population mean, E(Y), whereas, a single hypothesis test is a rejection rule for only one possible value of the population mean.

c) A confidence interval summarizes the set of hypothesis about the population mean, E(Y), you can and cannot reject at a given significance level.

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