Question

9. (10pts) NBC reports that Americans watch a mean of 30 minutes of television per evening. We conduct a research study in an attempt to prove that the mean is less. In a sample of 200 Americans, the sample mean was 24 minutes per evening with a standard deviation of 15 minutes.

(a) (2pts) Develop the null and alternative hypotheses:

(b) (2pts) Using α = 0.02, what is the rejection rule?

(c) (2pts) Find the test statistic.

(d) (2pts) Should H0 be rejected?

(e) (2pts) Based on your answer in part (d), what is your conclusion as it applies to THIS SITUATION?

Answer 1

Solution:

a)

H0: = 30

H1: < 30

b)

Given ,  α = 0.02

< sign in H1 , indicates that "Left tailed test"

n = 200

df = n - 1 = 200 - 1 = 199

Critical value for left tailed test is

Rejection rule : Reject H₀ if t < -2.067

c)

The test statistics t is given by ..

t =

= (24 - 30)/(15/200)

= -5.657

Test statistic t = -5.657

d)

Yes , H₀ should be rejected

(Because -5.657 is in the rejection region < 2.067)

e)

There is sufficient evidence to support the claim that the mean is less than 30 minutes.