Question

It is recommended that we get 8 hours of sleep on average per night! A random sample of 61 MCU students found for them that the average number of hours of sleep is 6.46 hours with a standard deviation of 1.68 hours. Do Marymount students sleep less than the recommended 8 hours? Use α = 0.05.

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 8
Alternative Hypothesis, Ha: μ < 8

Rejection Region
This is left tailed test, for α = 0.05 and df = 60
Critical value of t is -1.671.
Hence reject H0 if t < -1.671

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (6.46 - 8)/(1.68/sqrt(61))
t = -7.159

P-value Approach
P-value = 0
As P-value < 0.05, reject the null hypothesis.