Question

You are the manager of a restaurant for a fast-food franchise. Last month, the mean waiting time at the drive- through window for branches in your geographical region, as measured from the time a customer places an order until the time the customer receives the order, was 3.7 minutes. You select a random sample of 64 orders. The sample mean waiting time is 3.57 minutes, with a sample standard deviation of 0.8 minute.

1- At a 95% confidence level, is there evidence that the population mean waiting time is different from 3.7 minutes?

2- Because the sample size is 64, do you need to be concerned about the shape of the population distribution when conducting the t- test in (a)? Explain.

Answer 1

(2) A one sample t-test assumes that the underlying distribution is approximately a normal distribution. Here, since the sample size is 64, then according to the central limit theorem, the distribution of sample means is approximately normal. Hence, we do not need to be concerned about the shape of the population distribution because it is assumed to approximately follow a normal distribution.