Question

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 minute. We want to test to determine whether or not the mean waiting time of all customers is significantly more than 3 minutes.

Answer 1

The mean waiting time of all customers is significantly more than 3 minutes, at 0.05 significant level

Explanation:

Step 1: State the hypothesis and identify the claim.

`H_0:\mu=3\\H_1:\mu\:>\:3(claim)`

Step 2: We calculate the critical value. Since we were not given any significant level, we assume
`\alpha=0.05`, and since this is a right tailed test, the critical value is z=1.65

Step 3: Calculate the test statistic.

`Z=(\bar X-\mu)/((\sigma)/(√(n) ) )=(3.1-3)/((0.5)/(√(100) ) )=2`

Step 4:Decide. Since the test statistic , 2 s greater than the critical value, 1.65, and it is in the critical region, the decision is to reject the null hypothesis.

Step 5: Conclusion, there is enough evidence to support the claim that the mean is greater than 3