Paul W. answered • 29d
PhD in Statistics with 20+ Years of Math / Stat Education Experience
Cool question. Here's my answer:
A public bus company official claims that the mean waiting time for bus number 14 during peak hours is less than 10 minutes. Karen took bus 14 during peak hours on 18 different occasions. Her mean waiting time was 7.4 minutes. Assume that the standard deviation has been historically known to be 2.2. At the .05 significance level, test the claim that the mean waiting time is less than 10 minutes.
We're going to have to assume that wait time is normally distributed for this problem. Wait time is usually modeled better with an exponential distribution but we don't have an easy way to set that test up here. I'll make it easy and use the normal for this answer.
The problem indicates a one-tailed alternative; we want to test the null hypothesis that the true mean is ≤10 minutes against the alternative that μ > 10 minutes. This means that the p-value will be calculated as the area under the curve greater than or equal to the test statistic. The test statistic, based on the data, is:
T = sqrt(18) * (7.4 - 10)/2.2 = -5.014
This means that almost the entire curve is to the right of the observed test statistic and we do not have sufficient evidence to reject the claim that the wait time is under 10 minutes (p >> 0.05).
