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

Answer:

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

Step-by-step 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 = $\frac{s}{\sqrt{n} } \\=0.1273$

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

$H_0: \bar x = 7\\H_a: \bar x$

(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