Question

A survey conducted five years ago by the health center at a university showed that 5.9% of the students smoked cigarettes at the time. This year a new survey was conducted on a random sample of 600 students from this university, and it was found that 33 of them smoke cigarettes. Test the claim that the percentage of students who smoke cigarettes at this university is less than it was five years ago. Use a significance level of 0.02. a. Write the null and alternative hypotheses. Label the claim. b. Draw the graph and shade the critical area(s). Place the critical value(s) on the graph. C. Fill in the following: Critical Value(s) Test Statistic P Value d. Circle one: REJECT H or FAIL TO REJECT H. e. Statement of conclusion:

Answer 1

a)

The following null and alternative hypotheses need to be tested:

(claim)

Ho: p=0.059

Ha:p + 0.059

b)

Z-Test Results: Z-stats = -0.416, p-value =0.6775 0.40 0.35 0.30 0.25 0.20 0.15 0.10 0.05 0.00 -4.0 -3.5 -3.0 -2.5 -2.0-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 20 25 3.0 3.5 4.0

c)

Based on the information provided, the significance level is a = 0.02, and the critical value for a two- tailed test is 2c 2.33 =

The Z-statistic is computed as follows: - po Po(1 – po) n 0.055 – 0.059 0.059(1 – 0.059)/600 -0.416

p value = 2*p(z<-0.416) = 0.6775

d)

= 0.6775 > 0.02, it is Using the P-value approach: The p-value is p=0.6775, and since p concluded that the null hypothesis is not rejected.

e)

It is concluded that the null hypothesis Ho is not rejected. Therefore, there is not enough evidence to claim that the population proportion p is different than po, at the a = 0.02 significance level.