Question

What is the mean number of hours that high school students spend on homework per week? It is known that the standard deviation of the population is 2.2 hours. In a random sample of 40 students, it is found that they average 13 hours per week on homework.
a) What is the standard deviation for this sample?
b) What is the critical value for a 90% confidence interval?
c) What is the critical value for a 95% confidence interval?

Answer 1

This may help you

it is given that the standard deviation  0.8, so we can use  the normal distribution critical value for the 95% confidence interval. 
sample mean = 2.36 
standard deviation = 0.8 
standard error of mean = σ / √ n 
standard error of mean = 0.8 / √ 50 
se = 0.8/7.0711 
standard error of mean 0.1131 
Confidence interval 2.36-(0.1131)(1.96) 
and 2.36+(0.1131)(1.96) 
95% confidence interval :(2.14, 2.58)