Exhibit 9-2
The manager of a grocery store has taken a random sample of 100 customers. The average length of time it took the customers in the sample to check out was 3.1 minutes. The population standard deviation is known to be 0.5 minutes. We want to test to determine whether or not the mean waiting time of all customers is significantly more than 3 minutes.
-Refer to Exhibit 9-2. The p-value is
A)0.025
B)0.0456
C)0.05
D)0.0228

Question

Quizplus · Accepted Answer

To calculate the p-value, we need to use a one-sample t-test. The test statistic is calculated as follows:

t = (sample mean - hypothesized mean) / (sample standard deviation / sqrt(sample size))
t = (3.1 - 3) / (0.5 / sqrt(100)) 
t = 2

Using the t-distribution table with 99 degrees of freedom (100 - 1), we find the area in the right tail to be 0.0228. This is our p-value.

Since the p-value is less than the significance level of 0.05, we reject the null hypothesis and conclude that the mean waiting time of all customers is significantly more than 3 minutes.

Exhibit 9-2 The Manager of a Grocery Store Has Taken a Random