Question

A recent study shows that 83% of teenagers have used cell phones while driving. In Oct. 2010, Massachusetts enacted a law that forbids cell phone use by drivers under the age of 18. A policy analyst would like to test whether the law has lowered the proportion of drivers under the age of 18 who use a cell phone. In a random sample of 80 young drivers, 62 of them said that they used cell phones while driving. Test the policy maker's hypothesis at a significant level of 10%. (Round your steps to 4 decimal places, round the z test statistic to 2 decimal places) (12 points)

Answer 1

Answer:

Given,

p = 83% = 0.83

sample proportion p^ = x/n

substitute values

= 62/80

= 0.775

Null hypothesis Ho : p = 0.83

Alternative hypothesis Ha : p < 0.83

consider,

test statistic z = (p^ - p)/sqrt(p(1-p)/n)

substitute values

= (0.775 - 0.83)/sqrt(0.83(1-0.83)/80)

z = - 1.31

P value = P(z < - 1.31)

= 0.0950979 [since from z table]

P value = 0.0951

Here we observe that, p value < alpha, so we reject null hypothesis.

So there is sufficient evidence.