Teenage Tobacco Use: In a random sample of 1100 teenagers, 207 had used tobacco

Question

Teenage Tobacco Use: In a random sample of 1100 teenagers, 207 had used tobacco of some form in the last year. The managers of an anti-tobacco campaign want to claim that less than 20% of all teenagers use tobacco. Test their claim at the 0.10 significance level.

reject H0fail to reject H0    

(e) Choose the appropriate concluding statement.

The data supports the claim that less than 20% of all teenagers use tobacco.There is not enough data to support the claim that less than 20% of all teenagers use tobacco.    We reject the claim that less than 20% of all teenagers use tobacco.We have proven that less than 20% of all teenagers use tobacco.

Explanation / Answer

(a) What is the sample proportion of teenagers who use tobacco? Round your answer to 3 decimal places.
p = 207/1100 = 0.19

(b) Test Statistic

Z (p^) = (p - p0)/ sqrt [p0 * (1-p0)/ N] = (0.19 - 0.20)/ sqrt [ 0.19 * 0.81/ 1100] = 0.01/ 0.0118 = 0.85

(c) P - value = Pr (Z > 0.847) = 0.1977

(d) We will not be able to reject the null hypothesis because p - value > 0.10.

(e) We reject the claim that less than 20% of all teenagers uses tobacco. Option C is correct.

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