Question

a) The average nightly sleep time for adults is 7.4 hours a night with a standard deviation of 2.3 hours. A researcher suspects that college students’ sleep time may vary from this average. She surveys a sample of 12 college students and obtains the following nightly sleep times for this sample:

Participant/Sleep Time (hours)

A - 3

B - 4.5

C - 9

D - 7

E - 8

F - 5

G - 6

H - 4

I - 5

J - 6.5

K - 5

L - 4

Test the null hypothesis at the .05 level of significance. Use the step-by-step procedure illustrated in the text and in my class notes.

b) Even when you have conducted a hypothesis test correctly, statistical decisions are based on probability and therefore, they may be correct or in error. Suppose you have made an error in your decision for the hypothesis test in Part a of this question. Please answer the following questions about this error:

• What kind of error have you made?

• Can you determine the probability of this error? If yes, then indicate the probability of the error and how you determined the probability. If no, explain what factors would influence the probability of this error.

• What might you do in the future to decrease the probability of making this error?

Answer 1

Let denotes the average nightly sleep time for college students.

b) Since we reject the null hypothesis, one may make a Type I error (reject H₀ when H₀ is actually true).

P(Type I error) = level of significance = 0.05