You wish to test the following claim \( \left(H_{a}\right) \) at a significance level of \( \alpha=0.001 \). \[ \begin{array}{l}H_{o}: p_{1}=p_{2} \\ H_{a}: p_{1}<p_{2}\end{array} \] You obtain 134 successes in a sample of size \( n_{1}=203 \) from the first population. You obtain 316 successes in a sample of size \( n_{2}=436 \) from the second population. For this test, you should NOT use the continuity correction, and you should use the normal distribution as an approximation for the binomial distribution. What is the test statistic for this sample? (Report answer accurate to three decimal places.) test statistic: \( z= \) What is the p -value for this sample? (Report answer accurate to four decimal places.) P-value: \( p=\square \)

Construct a box plot from the given data. Diameters of Cans in an Assembly Line: \( 5.8,5.7,5.2,5.5,5.3,5.7,5.8,5.4,5.9,5.3 \)

Find the range of the following data set. Assume the data set is a sample.

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

A water bottling facility has a mean bottling rate of 33.5 thousand bottles per hour with a standard deviation of 1.92 thousand bottles. A nearby cola bottling facility has a mean bottling rate of 26.2 thousand bottles per hour with a standard deviation of 1.42 thousand bottles. One Wednesday from noon to \( 1: 00 \) p.m., the water bottling facility bottled 36.8 thousand bottles of water, and the cola bottling facility bottled 28.4 thousand bottles of cola. Which facility increased their efficiency more during that hour? Answer

Scores on a test have a mean of 78 and a standard deviation of 13 . Tom has a score of 66 . Convert Tom's score to a \( z \)-score, rounded to the nearest hundredth.