Question

You are interested in the effect of energy drinks on the amount of hours of sleep students get each night. Specifically, you expect that energy drinks will decrease the average amount of sleep a student gets. To investigate this, you gather a sample of 15 students that drink energy drinks each night for a week and get their average reported hours of sleep per night and compare it to the average amount of sleep for all students. The data are below:

Students w/ Energy Drinks	All Students
x ̅=6.8	µ=8.2
s = 1.5

Do you reject or fail to reject your hypothesis? Why?

		We reject, because our test statistic falls within the rejection rejection
		We fail to reject, because our test statistic does not fall within the rejection region
		We reject, because our test statistic is not different from the critical value.
		We fail to reject, because the test statistic is different from the critical value.

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 8.2
Alternative Hypothesis, Ha: μ < 8.2

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (6.8 - 8.2)/(1.5/sqrt(15))
t = -3.615

Rejection Region
This is left tailed test, for α = 0.05 and df = 14
Critical value of t is -1.761.
Hence reject H0 if t < -1.761

We reject, because our test statistic falls within the rejection rejection