Question

multiple choice 4 points
select the most appropriate response.
five years ago, a survey found that the proportion of city employees who commute to work by car is 8%. a local city commissioner claims
that the percentage is higher than it was five years ago. data on employee commuting by car was collected on a random sample of 1000
employees and found 12% of employees commute by car. test an appropriate hypothesis and state your conclusion at the 10% level of
significance.
state the alternative hypothesis, the test statistic, your decision and your findings
note: the p - value is 0.00000156.
$h_a:p = 0.08$; $z = 4.66$; do not reject the null hypothesis. this data does not show a proportion in car commuting greater than 8%.
$h_a:p>0.08$; $z = 4.66$; reject the null hypothesis. this data shows a proportion in car commuting greater than 8%.
$h_a:p<0.08$; $z = - 4.66$; reject the null hypothesis. this data does not show a proportion in car commuting greater than 8%.
$h_a:p>0.08$; $z = - 4.66$; do not reject the null hypothesis. this data shows a proportion in car commuting greater than 8%.
$h_a:p<0.08$; $z = 4.66$; reject the null hypothesis. this data does not show a proportion in car commuting greater than 8%.

Explanation:

Step1: Determine the alternative hypothesis

Since the claim is that the percentage is higher than it was five years ago (where it was 8%), the alternative hypothesis \(H_A:p > 0.08\).

Step2: Make a decision using the p - value

The significance level \(\alpha=0.10\). The p - value is \(0.00000156\). Since \(p - value=0.00000156<\alpha = 0.10\), we reject the null hypothesis.

Answer:

\(H_A:p > 0.08\); \(z = 4.66\); Reject the null hypothesis. This data shows a proportion in car commuting greater than 8%.