Question

A 2017 study selecting a sample of 300 cars traveling daily on a highway revealed that 170 were driven by women. With a significance level of 90% find the confidence interval for the sample indicated.

According to a 2010 study, 52 out of every 100 drivers are female. Based on the results of the constructed interval, can you conclude that more women will be driving on the highway in 2017 than indicated in the 2010 study?

Answer 1

Solution:

Given that

n= 300 sample size of cars traveling daily on highway.

X = 170 cars driven by women.

sample proportion of cars driven by women on daily highway.

The 90% confidence interval for population proportion is

At

. From Z table

( 0.57 - 0.0468764 , 0.57 + 0.0468764)

( 0.523123, 0.6168764)

( 0.5231, 0.6169)

The 90% confidence interval for population proportion is

( 0.5231, 0.6169)

The proportion of cars drivers are Female in 2010 study is

The proportion of cars drivers are female in 2010 study is p=0.52 is outside the confidence interval created in 2017 study . Then we conclude that more women will be driving on the highway in 2017 than indicated in the 2010 study.