complete question
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 α = 0.05 has the law been effective?
d. Repeat this exercise using the critical value approach with α = 0.05
Answer:
1. H0: p>=0.82
H1: p<0.82
2. z test statistic = -2.5767
3. the law has been effective
4. the null is rejected, the law has been effective
Step-by-step explanation:
1. hypothesis formulation
H0: p>= 0.82
H1: p< 0.82
2. p = 82% = 0.82
estimated p^ = x/n = 150/200 = 0.75
standard error calculation:
= √0.82(1-0.82)/200
= √0.82x0.18/200
= √0.02716615
Z test statistic calculation:
= 0.75-0.82/0.02716615
= -2.5767
3. this test is 1 tailed
the p-value using a p value calculator is = 0.004983
0.004983 < 0.05 so we Reject null and conclude that the law has been effective.
4. we Reject null at 0.05 if z is less than -1.645.
-2.5767<-1.645 so we Reject H0 and conclude law has been effective and there is a decrease in drivers under this age who use cell phones
