91Ó°ÊÓ

A consumer testing agency plans to calculate a \(99 \%\) confidence interval for the mean mpg for all cars on the road in 2019. Suppose the mpg measurements for the population of interest is actually sharply skewed right. For which of the sample sizes, \(n=30,50,\) or \(70,\) would the sampling distribution of \(\bar{x}\) be closest to normal? (A) 30 (B) 50 (C) 70 (D) Because of skewness of the population, none of the sampling distributions can be approximately normal. (E) Because of the central limit theorem, all sampling distributions with \(n \geq 30\) are equally approximately normal.

Suppose (25,30) is a \(90 \%\) confidence interval estimate for a population mean \(\mu\). Which of the following is a true statement? (A) There is a 0.90 probability that \(\bar{x}\) is between 25 and \(30 .\) (B) Of the sample values, \(90 \%\) are between 25 and 30 . (C) There is a o.9o probability that \(\mu\) is between 25 and 30 . (D) If 100 random samples of the given size are picked and a \(90 \%\) confidence interval estimate is calculated from each, \(\mu\) will be in 90 of the resulting intervals. (E) If \(90 \%\) confidence intervals are calculated from all possible samples of the given size, \(\mu\) will be in \(90 \%\) of these intervals.

Suppose you do five independent tests of the form \(H_{0}: \mu=38\) versus \(H_{a}: \mu>38,\) each at the \(\alpha=0.01\) significance level. What is the probability of committing a Type I error and incorrectly rejecting a true null hypothesis with at least one of the five tests? (A) 0.01 (B) 0.049 (C) 0.05 (D) 0.226 (E) \(0.95^{1}\)