Question

The author obtained times of sleep for randomly selected adult subjects included in the National Health and Nutrition Examination Study, and those times (hours) are listed below.

  4, 7,   4, 4, 8, 6, 8, 7, 7, 6, 7, 6.

A common recommendation is that adults should sleep between 7 hours and 9 hours each night. Use 0.05 significance level to test the claim that the mean amount of sleep for adults is less than 7 hours.

		Reject . There is sufficient evidence to support the claim that the mean amount of sleep for adults is less than 7 hours.
		Reject . There is not sufficient evidence to support the claim that the mean amount of sleep for adults is less than 7 hours.
		Do not reject  . There is not sufficient evidence to support the claim that the mean amount of sleep for adults is less than 7 hours.
		Do not reject  . There is sufficient evidence to support the claim that the mean amount of sleep for adults is less than 7 hours.

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 7
Alternative Hypothesis, Ha: μ < 7

Rejection Region
This is left tailed test, for α = 0.05 and df = 11
Critical value of t is -1.796.
Hence reject H0 if t < -1.796

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (6.1667 - 7)/(1.4668/sqrt(12))
t = -1.968

P-value Approach
P-value = 0.0374
As P-value < 0.05, reject the null hypothesis.

Reject . There is sufficient evidence to support the claim that the mean amount of sleep for adults is less than 7 hours.