To test \( \mathrm{H}_{0}: \mu=20 \) versus \( \mathrm{H}_{1}: \mu<20 \), a simple random sample of size \( n=16 \) is obtained from a population that is known to be normally distributed. Answer parts (a)-(d). Click here to view the t-Distribution Area in Right Tail. (d) If the researcher decides to test this hypothesis at the \( \alpha=0.05 \) level of significance, will the researcher reject the null hypothesis? B. The researcher will reject the null hypothesis since the P-value is not less than \( \alpha \). C. The researcher will not reject the null hypothesis since the P-value is less than \( \alpha \). D. The researcher will not reject the null hypothesis since the P-value is not less than \( \alpha \).

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

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

Scores on a test have a mean of 89 and a standard deviation of 7 . Calvin has a score of 79. Convert Calvin's score to a \( z \)-score, rounded to the nearest hundredth.

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

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.