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.