Question

A school psychologist reports that the mean number of hours the students at this school sleep each night is 8 hours. the students believe the mean is not 8 hours. to find an estimate of the true mean, they select a random sample of 15 students from their school and ask how many hours each slept last night. a stemplot and boxplot of the numbers of hours are shown here. t he sample mean is 6.67 hours with a sample standard deviation of 1.88 hours.
a. verify that the conditions for computing a confidence interval are met in this case.
b. compute and interpret a 95% confidence interval for the mean number of hours the students at this school sleep each night.

Answer 1

a. verify that the conditions for computing a confidence interval are met in this case.
The formula for computing the CI interval is given by:
x_bar+/-z (s/√n)
since:
x_bar=6.67
s=1.88
n=15
The conditions are met because we have all the values necessary for computing CI.

b]  compute and interpret a 95% confidence interval for the mean number of hours the students at this school sleep each night.
The value of z corresponding to 95% CI is 1.96
thus the 95% CI will be:
6.67+/-1.96(1.88/√15)
=6.67+/-1.96(0.4854)
=6.67+/-0.9514