Question

8. Page 4 of 8 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.

Answer 1

Given Data in problem

Survey done 5 years ago and population proportion of student found smoking in university = 5.9%

p = 0.059

New survey

Sample size = n = 600

Student found smoking = X = 33

Sample proportion

$p' = \frac{X}{n} = \frac{33}{600} = 0.055$

(a)Since we have to test the claim that the percentage of students smokes cigarette in university is less than it was 5 years ago, So null and alternative hypotheses need to be tested

Ho: p ≥ 0.059

Ha: p < 0.059[CLAIM]

This corresponds to a left-tailed test

At the significance level is α=0.02, and the critical value for a left-tailed test is zc​=−2.05 using excel =NORM.S.INV(0.02)

The rejection region for this left-tailed test is R = z<−2.05

(b)Test Statistics

الا - با ( 2 5 == 2.05

$z = \frac{p'-p}{\sqrt{\frac{p(1-p)}{n}}}$

$z = \frac{0.055-0.059}{\sqrt{\frac{0.059(1-0.059)}{600}}}$

P value is calculated for corresponding z value using excel =NORM.S.DIST(-0.416,TRUE) is p = 0.3388

(c) Critical value = - 2.05

Test statistics = - 0.416

p value = 0.3388

(d)Since it is observed that z = -0.416 is greater than zc​=−2.05, it is then concluded that the null hypothesis is not rejected.

So Fail to reject Ho

(e)Conclusion

It is concluded that the null hypothesis Ho is not rejected. Therefore, there is not enough evidence to support the claim that claim that the percentage of students smokes cigarette in university is less than it was 5 years ago at α=0.02 significance level.