Question

New York State law requires tobacco sellers not to sell to anyone under 18 years of age, and to seek proof of age from anyone looking 25 years of age or less. In May 1994, the Suffolk County Department of Health conducted an undercover operation to see if sellers were complying with this law. Using operatives between 13 and 17 years of age, they visited 130 selling locations, sending in one operative at each to try to buy cigarettes. In 56 of the locations, the operative was successful in purchasing cigarettes.

(a) Is the probability that a randomly selected Suffolk County tobacco seller will sell cigarettes to an underage buyer larger than 0.5 at 1% level of significance?
(b) A local newspaper report states that “A good estimate of the probability that a randomly chosen typical underage teen will be able to successfully purchase cigarettes is .431.” Is this a correct statement?

Answer 1

a)

Proportion (p0) = 0.5

Total number of sample (n) = 130

number of favourable events (X) = 56

We are interested in testing the hypothesis

Since P-value of a two tailed test is equal to

P = (1-0.057202442416180076)

P = 0.9428

Since, the test is two-tail test at \alpha = 0.01

Decision Rule: Reject the null hypothesis if the test statistic value is greater than the critical value 2.33

The statistic value, -1.5787 is less than the critical values 2.33. Therefore, we fail to reject the null hypothesis.

No, as the probability that a randomly selected Suffolk County tobacco seller will sell cigarettes to an underage buyer smaller than 0.5 at 1% level of significance

b) The statement is correct