Question

(Round all intermediate calculations to at least 4 decimal places.)

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. Use Table 1 and Table 2.

a.	Select the null and the alternative hypotheses to test the policy analyst’s objective.
	H0: p = 0.82; HA: p ≠ 0.82 H0: p ≤ 0.82; HA: p > 0.82 H0: p ≥ 0.82; HA: p < 0.82

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? (Negative values should be indicated by a minus sign. Round your answer to 2 decimal places.)

Test statistic

	The p-value is:
	p-value < 0.01 0.01 ≤ p-value < 0.025 0.025 ≤ p-value < 0.05 0.05 ≤ p-value < 0.10 p-value ≥ 0.10

  

c.	At α = 0.05, do you reject the null hypothesis?
	Yes, since the p-value is greater than α. Yes, since the p-value is smaller than α. No, since the p-value is greater than α. No, since the p-value is smaller than α.

  

Test using the critical value approach with α = 0.05.

d-1.	Calculate the critical value. (Negative value should be indicated by a minus sign. Round your answer to 2 decimal places.)

Critical value

d-2.	What is the conclusion?
	The law has been effective since the value of the test statistic falls in the rejection region. The law has not been effective since the value of the test statistic falls in the rejection region. The law has been effective since the value of the test statistic does not fall in the rejection region. The law has not been effective since the value of the test statistic does not fall in the rejection region.

Answer 1

The statistical software output for this problem is:

Hence,

a) H₀: p ≥ 0.82; H_A: p < 0.82

b) Test statistic = -2.58

p-value < 0.01

c) Yes, since the p-value is smaller than α.

d - 1) Critical value = -1.65

d - 2) The law has been effective since the value of the test statistic falls in the rejection region.