A recent study by Allstate Insurance Co finds that 82 of tee

A recent study by Allstate Insurance Co. finds that 82% of teenagers have used cell phones while driving ( The Wall Street Journal , May 5, 2010). In October 2010, Massachusetts enacted a law that forbids cell phone use by drivers under the age of 18. A policy analyst would like to determine whether the law has decreased the proportion of drivers under the age of 18 who use a cell phone.
a. State the null and the alternative hypotheses to test the policy analyst’s objective.
b. Suppose a sample of 200 drivers under the age of 18 results in 150 who still use a cell phone while driving. What is the value of the test statistic? What is the p-value?
c. At = 0.05 has the law been effective?
d. Repeat this exercise using the critical value approach with = 0.05.

A recent study by Allstate Insurance Co. finds that 82% of teenagers have used cell phones while driving ( The Wall Street Journal , May 5, 2010). In October 2010, Massachusetts enacted a law that forbids cell phone use by drivers under the age of 18. A policy analyst would like to determine whether the law has decreased the proportion of drivers under the age of 18 who use a cell phone.
a. State the null and the alternative hypotheses to test the policy analyst’s objective.
b. Suppose a sample of 200 drivers under the age of 18 results in 150 who still use a cell phone while driving. What is the value of the test statistic? What is the p-value?
c. At = 0.05 has the law been effective?
d. Repeat this exercise using the critical value approach with = 0.05.

Formulating the null and alternatuve hypotheses,

Ho:   p   >=   0.82
Ha:   p   <   0.82 [ANSWER]

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As we see, the hypothesized po =   0.82
Getting the point estimate of p, p^,

p^ = x / n =    0.75

Getting the standard error of p^, sp,

sp = sqrt[po (1 - po)/n] =    0.027166155

Getting the z statistic,

z = (p^ - po)/sp =    -2.576735608   [ANSWER, TEST STATISTIC]

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c)

As this is a    1   tailed test, then, getting the p value,

p =    0.00498691

As P < 0.05, then we reject Ho. YES, THE LAW HAS BEEN EFFECTIVE.

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At 0.05 left tailed test, we reject Ho if

z < -1.645.

Thus, as z < -1.645 here, then we reject Ho.

There is significant evidence that the proportion of those who use cellphone while driving has decreased. [CONCLUSION]