Question

In a random sample of 900 teenagers, 148 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 0.01 significance level. (a) What is the sample proportion of teenagers who use tobacco? Round your answer to 3 decimal places. p̂ = (b) What is the test statistic? Round your answer to 2 decimal places. zp hat = (c) What is the P-value of the test statistic? Round your answer to 4 decimal places. P-value = (d) What is the conclusion regarding the null hypothesis? reject H0 fail 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.

Answer 1

a) = 148/900 = 0.164

b) The test statistic is

  

c) P-value = P(Z < -2.7)

               = 0.0035

d) The P-value is less than

Reject H₀.

e) The data supports the claim that less than 20% of all teenagers use tobacco.