Last month the waiting time at the drive through window of a fast-food restaurant was 3.7 minutes

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Question:

Last month the waiting time at the drive-through window of a fast-food restaurant was 3.7 minutes. The franchise has installed a new process intended to reduce waiting time. After the installation, a random sample of 64 orders is selected. The sample mean waiting time is 3.57 minutes with a sample standard deviation of 0.8 minutes. At a 5% level of significance, is there sufficient evidence that the population mean waiting time is now less than 3.7 minutes? What is your conclusion?

Given:

The franchise has installed a new process intended to reduce waiting time. After the installation of new process, test if there is sufficient evidence that the population mean waiting time is now less than 3.7 minutes.

Step 1) State H0 and Ha

H_{0}: \mu = 3.7 \: \: \: \: Vs\: \: \: H_{a}: \mu < 3.7