You are the manager of a fast-food restaurant. You claim that the average waitin

Question

You are the manager of a fast-food restaurant. You claim that the average waiting time for a customer in your store is 4.5 minutes. However, a number of disgruntled customers have called your regional headquarters to complain that your service was too slow, inspiring the regional manager to conduct a hypothesis test in which he can prove that the average waiting time is actually more than 4.5 minutes. He observes the store and collects data on 100 customers' waiting times. The average waiting time for this sample is 4.7 minutes, and the population standard deviation is 1.2 minutes. At a level of significance of 0.05, he will draw his conclusion. After performing his test, he records the significant numerical values below. Data: Hypothesized mean . 4.5 Sample mean 4.7 Population standard deviation 1.2 Calculations: z-test statistic 1.67 p-value 0.0475 What is his conclusion? reject the null, the mean waiting time is more than 4.5 minutes reject the null, the mean waiting time is not more than 4.5 minutes fail to reject the null, the mean waiting time is more than 4.5 minutes fail to reject the null, the mean waiting time is not more than 4.5 minutes

Explanation / Answer

Given information:

Sample mean = 4.7 minutes

Sample size = 100

Population statndard deviation = 1.2

Level of significance = 0.05

And

H0: the average waiting time is not more than 4.5 minutes. that is <= 4.5

H1: the average waiting time is actually more than 4.5 minutes.that is > 4.5

Z test statistics = 1.67

P value = 0.0475

Here p value less than 0.05 hence we reject null hypothesis that says, the average waiting time is not more than 4.5 minutes. that is at at 5% level of significance evidence shows that

the average waiting time is actually more than 4.5 minutes.

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