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 81 orders. The sample mean waiting time is 3.41 minutes, with a sample standard deviation of 0.9 minute. At the 0.01 level of significance, is there evidence that the population mean waiting time is different from 3.7 minutes? State the null and alternative hypotheses. Determine the test statistic.(two decimal places) Find the p-value.(three decimal places) What is the conclusion? Do i need to be concerned about the shape of the population distribution?

Answer #1

To Test :-

H0 :- µ = 3.7

H1 :- µ ≠ 3.7

Test Statistic :-

t = ( X̅ - µ ) / ( S / √(n))

t = ( 3.41 - 3.7 ) / ( 0.9 / √(81) )

**t = -2.90**

Decision based on P value

**P - value = P ( t > 2.9 ) = 0.0048 ≈
0.005**

Reject null hypothesis if P value < α = 0.01 level of
significance

P - value = 0.0048 < 0.01 ,hence we reject null hypothesis

**Conclusion :- Reject null hypothesis**

There is sufficient evidence to support the claim that mean waiting time is different from 3.7 minutes.

Since the sample is large enough, we can consider the population to be normally distributed.

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