Question

A survey of 1000 drivers found that 29% of the people send text messages while driving. Last year, a survey of 1000 drivers found that 17% of those sent text messages while driving.

1.) Give a 95% confidence interval for the increase in text messaging while driving.   

2.) At α = .0 5 , can we conclude that there has been an increase in the number of drivers who text while driving? State the hypotheses, find the test statistic, and state your conclusion and the reasoning behind it.   

Answer 1

1)

95% confidence interval for p is

- Z/2 * sqrt( ( 1 - ) / n) < p < + Z/2 * sqrt( ( 1 - ) / n)

0.29 - 1.96 * sqrt( 0.29* 0.71 / 1000) < p < 0.29 + 1.96 * sqrt( 0.29* 0.71 / 1000)

0.262 < p < 0.318

95% CI is ( 0.262 , 0.318 )

2)

H0: p = 0.17

Ha: p > 0.17

Test statistics

z = - p / sqrt( p( 1 - p) / n)

= 0.29 - 0.17 / sqrt( 0.17 * 0.83 / 1000)

= 10.10

This is test statistics value.

Critiacl value at 0.05 level is 1.645

Since test statistics z > 1.645, we have sufficient evidence to reject H0.

We conclude at 0.05 level that we have enough evidence to support the claim.