You are considering moving to Richmond Hill and are concerned about the average one-way commute time to downtown Toronto.Does the average one-way commute time exceed 25 minutes? You take a random sample of 100 Richmond Hill residents and find an average commute time of 29 minutes with a standard deviation of 7 minutes.

Question

Quizplus · Accepted Answer

We can use a one-sample t-test with a significance level of 0.05 to test whether the average commute time for Richmond Hill residents is significantly higher than 25 minutes. The null hypothesis is that the true population mean commute time is equal to 25 minutes, and the alternative hypothesis is that it is greater than 25 minutes.

Using the sample data, we calculate the t-statistic as (29-25)/(7/sqrt(100)) = 4.57. The degrees of freedom are n-1 = 99. Checking the t-distribution table with 99 degrees of freedom at a significance level of 0.05, the critical value is 1.660.

Since our calculated t-statistic (4.57) is greater than the critical value (1.660), we reject the null hypothesis and conclude that the average one-way commute time in Richmond Hill is significantly greater than 25 minutes. Therefore, choice B is the best answer.

You Are Considering Moving to Richmond Hill and Are Concerned