Question

A recent study shows that 83% of teenagers have used cell phones while driving. In Oct. 2010, California 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)

Answer 1

Answer :

We have given :

n = sample size = 80

x = 62   of them said that they used cell phones while driving

phat = sample proportion = x / n = 62 / 80 = 0.775

p = population proportion = 83 %

## Hypothesis test for claimed :

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.

## Step 1 ) To test :

Ho : p = 0.83   Vs   H1 : p <  0.83

( it is left tailed test )

## Step 2 ) Test Statistics :

z = ( phat - p ) / SQRT( p * (1-p) / n)

z = ( 0.775  - 0.83 ) / SQRT ( (0.83 * 0.17 ) / 80 )

z = ( - 0 .055 ) / 0.04199 = - 1 . 3096166 ie

= - 1.3096

## Step 3 ) α = level of significance value = 10 % = 0.10

## Step 4 ) p value = P [ z < - 1.3096 ] ( using statistical table )

= 0.0952  

## Step 5) z critical value = - 1.28 ( from statistical table )  

## Step 6) Decision :

We reject Ho if p value is less than α value using p value approach   here p value is less   than α value we

reject Ho at given level of significance .

## Step 7 ) Conclusion :

There is sufficient evidence to conclude that the law has lowered the proportion

of drivers under the age of 18 who use a cell phone