A simple random sample of size \( n=15 \) is drawn from a population that is normally distributed. The sample mean is found to be \( \bar{x}=27.4 \) and the sample standard deviation is found to be \( s=6.3 \). Determine if the population mean is different from 24 at the \( \alpha=0.01 \) level of significance. Complete parts (a) through (d) below. (a) Determine the null and alternative hypotheses. \( \mathrm{H}_{0}: \quad \mu \quad=24 \) \( \mathrm{H}_{1}: \quad \mu \quad \neq 24 \) (b) Calculate the P-value. P-value \( =\square \) (Round to three decimal places as needed.)

Find the range of the following data set, Assume the data set is a sample. \[ \begin{array}{lllllllllll} & 41 & 82 & 37 & 43 & 77 & 44 & 44 & 50 & 49 & 49\end{array} \] 8

A water bottling facility has a mean bottling rate of 35.2 thousand bottles per hour with a standard deviation of 2.04 thousand bottles, A nearby cola bottling facility has a mean bottling rate of 26.9 thousand bottles per hour with a standard deviation of 1.51 thousand bottles. One Wednesday from noon to \( 1: 00 \) p.m., the water bottling facility bottled 36.9 thousand bottles of water, and the cola bottling facility bottled 27.9 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.

Identify the population, the sample, and any population parameters or sample statistics in the given scenario. In the 1960 s, a poll of 2617 homeowners in the United States resulted in a report that the average price of a house in the U.S. was \( \$ 18,500 \). Answer O Population: none given: Sample: 2617 homeowners polled: Sample Statistic: \( \$ 18,500 \) Opopulation: U.S. homeowners: Sample: none given; Population Parameter: \( \$ 18,500 \)

In how many ways can a committee of 5 students be formed from 10 students?