Question

Chegg in order to determine how many hours per week freshmen college students watch television, a random sample of 256 students was selected. it was determined that the students in the sample spent an average of 14 hours watching television. the standard deviation the population is 3.2 hours per week for all freshman college students. provide a 95% confidence interval estimate for the average number of hours that all college freshmen spend watching tv per week.

Answer 1

The confidence interval is given by
$14\pm0.392$ or (13.608,14.392).

We first calculate the z-score associated with this level of confidence:
Convert 95% to a decimal:  95% = 95/100 = 0.95
Subtract from 1:  1-0.95 = 0.05
Divide by 2:  0.05/2 = 0.025
Subtract from 1:  1-0.025 = 0.975

Using a z-table (http://www.z-table.com) we see that this value has a z-score of 1.96.  

The formula for the confidence interval is
$\overline{x}\pm z*\frac{\sigma}{\sqrt{n}} \\ \\14\pm 1.96*(\frac{3.2}{\sqrt{256}})=14\pm 1.96*(\frac{3.2}{16})=14\pm 0.392$