Question

. At a local university, the professor of sleep would like to know the mean time a college student sleeps per nite. Ten randomly selected students were asked how long they slept at night. The mean time they slept was 7.1 hours, and the standard deviation was 0.78 hour.

a) Find the best point estimate for the true mean time: ______________

b) Find the 95% confidence interval for the population mean: ______________________

c) A second professor believes that the mean number of hours a student sleeps

is about 8.5 hours. Based on the confidence interval above would you agree or disgree and explain.

Answer 1

a) The best point estimate for the true mean is equal to the sample mean which is 7.1 hours here. Therefore the best point estimate for the true mean is 7.1 hours.

b) For n - 1 = 9 degrees of freedom, we get from the t distribution tables that:
P( -2.262 < t₉ < 2.262) = 0.95

Therefore the confidence interval here is obtained as:

This is the required 95% confidence interval for the population mean.

c) As the value of 8.5 hours lies above the whole confidence interval, therefore based on the above interval, we would reject the professor claim here and conclude that we have sufficient evidence that the mean number of hours a student sleeps is not 8.5 hours.