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 3.6 minutes. You select a random sample of 81 orders. The sample mean waiting time is 3.79 ​minutes, with a sample standard deviation of 0.9 minute. At the 0.10 level of​ significance, is there evidence that the population mean waiting time is different from 3.6 ​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

Solution :

This is the two tailed test .

The null and alternative hypothesis is ,

H0 :   = 3.6

Ha : 3.6

Test statistic(t) =

= ( - ) / s / n

= (3.79 - 3.6) /0.9 / 81

Test statistic = 1.9

P(z > 1.9) = 2 * [1 - P(z < 1.9)] = 2 * 0.0287

P-value = 0.0574

= 0.10

P-value <

Reject the null hypothesis .

There is sufficient evidence to support the population mean waiting time is different from 3.6 minutes.