Question

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.

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? (Negative values should be indicated by a minus sign. Round your intermediate calculations to 4 decimal places. Round "test statistic" to 2 decimal places and "p-value" to 4 decimal places.)

Test using the critical value approach with ? = 0.05. critical value=?

Answer 1

Test statistic = 2.29

p-value = 0.0110

The proportion of teenagers that have used cell phones while driving is less than 0.82.

Critical value = 1.645

Explanation:

H0: mu = 0.82

Ha: mu < 0.82

Test statistic (z) = (p' - p) ÷ sqrt[p(1-p) ÷ n]

p' is the population proportion = 82% = 0.8200

p is sample proportion = 150/200 = 0.7500

n is number of drivers sampled = 200

z = (0.8200 - 0.7500) ÷ sqrt[0.7500(1 - 0.7500) ÷ 200] = 0.0700 ÷ 0.0306 = 2.29 (to 2 decimal places)

p-value = 1 - cumulative area of test statistic = 1 - 0.9890 = 0.0110

The test is a one-tailed test because the alternate hypothesis is expressed using less than. With a 0.05 significance level, critical value is 1.645.

Conclusion:

Reject the null hypothesis H0 because the test statistic 2.29 is greater than the critical value 1.645.

There is sufficient evidence to conclude that the proportion of teenagers that have used cell phones while driving is less than 0.82