Question

According to a recent survey, Americans get a mean of 7 hours of sleep per night. A random sample of 50 students at West Virginia University revealed the mean length of time slept last night was 6 hours and 48 minutes (6.8 hours). The standard deviation of the sample was 0.9 hours.

At the 5% level of significance, is it reasonable to conclude that students at West Virginia sleep less than the typical American?

Answer 1

At the 5% level of significance, it is not reasonable to conclude that students at West Virginia sleep less than the typical American

Explanation:

Given that according to a recent survey, Americans get a mean of 7 hours of sleep per night. A random sample of 50 students at West Virginia University revealed the mean length of time slept last night was 6 hours and 48 minutes (6.8 hours). The standard deviation of the sample was 0.9 hours.

n =50

Std error =
`(s)/(√(n) ) \\=0.1273`

Since sample std dev is only known, we can use t test.

`H_0: \bar x = 7\\H_a: \bar x <7`

(left tailed test at 5% level)

Mean difference = -0.12

Test statistic t = mean diff/std error = -0.9429

p value for t test with d f= 49 is 0.175

Since p>alpha we accept null H0

At the 5% level of significance, it is not reasonable to conclude that students at West Virginia sleep less than the typical American