Previously, $8.6 \%$ of workers had a travel time to work of more than 60 minutes. An urban economist believes that the percentage has increased since then. She randomly selects 60 workers and finds that 8 of them have a travel time to work that is more than 60 minutes. Test the economist's belief at the $\alpha=0.05$ level of significance.

Find the P-value.
P-value $=\square$ (Round to three decimal places as needed.)

Step 1 ：This is a problem of hypothesis testing for a proportion. The null hypothesis is that the proportion of workers with a travel time of more than 60 minutes is still 0.086 (8.6%), and the alternative hypothesis is that the proportion has increased.

Step 2 ：The test statistic is the number of workers in the sample with a travel time of more than 60 minutes, which follows a binomial distribution under the null hypothesis.

Step 3 ：The P-value is the probability of observing a test statistic as extreme or more extreme than the one observed, under the null hypothesis. In this case, it is the probability of observing 8 or more workers with a travel time of more than 60 minutes, if the true proportion is still 0.086.

Step 4 ：Given that the sample size (n) is 60, the proportion (p) is 0.086, and the number of workers with a travel time of more than 60 minutes (k) is 8, we can calculate the P-value.

Step 5 ：The P-value is approximately 0.141, which is greater than the significance level of 0.05. This means that we do not reject the null hypothesis.

Step 6 ：The data does not provide strong evidence to support the economist's belief that the proportion of workers with a travel time of more than 60 minutes has increased.

Step 7 ：Final Answer: The P-value is approximately \(\boxed{0.141}\).