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 \(\boxed{0.141}\).