You wish to test the following claim \( \left(H_{a}\right) \) at a significance level of \( \alpha=0.001 \). \( \begin{array}{l}H_{o}: \mu=72.3 \\ H_{a}: \mu>72.3\end{array} \) You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size \( n=274 \) with mean \( M=77 \) and a standard deviation of \( S D=19.3 \). What is the test statistic for this sample? (Report answer accurate to three decimal places.) test statistic = What is the p -value for this sample? (Report answer accurate to four decimal places.) p -value \( = \)

Suppose that shoe sizes of American women have a bell-shaped distribution with a mean of 8.06 and a standard deviation of 1.52 . Using the empirical rule, what percentage of American women have shoe sizes that are greater than 9.58 ? Please do not round your answer.

The grades on the second statistics test for Ms. Rose's class are in the following list. Find the frequency distribution for the grades. \[ \text { F, D, F, B, F, A, C, F, C, F, D, B, B, B, C, C, F, C, F, D, A } \]

The grades on the second statistics test for Mr. Brown's class are in the following list. Find the frequency distribution for the grades. \[ \text { C, D, B, F, B, A, F, F, B, B, B, F, D, B, F, D, F, B, F, B, C } \]

A water bottling facility has a mean bottling rate of 34.1 thousand bottles per hour with a standard deviation of 2.13 thousand bottles. A nearby cola bottling facility has a mean bottling rate of 25.7 thousand bottles per hour with a standard deviation of 1.63 thousand bottles. One Wednesday from noon to \( 1: 00 \) p.m., the water bottling facility bottled 37.2 thousand bottles of water, and the cola bottling facility bottled 27.7 thousand bottles of cola. Which facility increased their efficiency more during that hour? Answer

Find the range of the following data set. Assume the data set is a sample. \[ 43 \quad \begin{array}{lllllllll}54 & 51 & 86 & 39 & 51 & 52 & 45 & 81 & 46\end{array} 46 \]