Question

The National Collegiate Athletic Association reported that the mean number of hours spent per week on coaching and recruiting by college football assistant coaches during the season was 45 hours. You are not sure their claim is correct so you gather a random sample of data from 40 assistant coaches showing the sample mean to be 42 hours with a standard deviation of 7.2 hours. use the sample data to construct a 99% confidence interval for the population mean.
(round to four decimal places as needed)

a. what is the margin of error
(rounded to four decimal places as needed)

b. what is the confidence interval?

c. does the claim appear to be reasonable?

Answer 1

A sample of n = 50 assistant show-ed that the sample mean number of hours spent per week on coaching Xbar = 42 with a standard deviation of s = 8.2 hours per week. Population mean is estimated to be = 45 hours.

a.

find the margin of error for the sample size n=50, standard deviation σ=36/5, and confidence level 99.0% using t-distribution.

First, find the critical value: t=2.680

Next, find the standard error of the mean:

Finally, the margin of error is

Answer: ME=2.7288

b.

The provided sample mean is Xbar=42 and the population standard deviation is σ=7.2. The size of the sample is n=50 and the required confidence level is 99%.

the critical z-value for α=0.01 is zc​=2.576.

The 99% confidence for the population mean μ is computed using the following expression

the 99 % confidence for the population mean μ is

c. Changing the level of confidence from 99 percent to 95 percent would increase the width of the confidence interval. The change in the value of t from 2.680 to 2.010 would increase the width of the interval.

Increase the interval