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 64 orders. The sample mean waiting time is 3.82 ​minutes, with a sample standard deviation of0.8 minute. Complete parts​ (a) and​ (b) below.

a. At the 0.05 level of​ significance, is there evidence that the population mean waiting time is different from 3.6 minutes? State the null and alternative hypotheses.

H0​: μ

H1: μ

Determine the test statistic.

The test statistic is ______

(Round to two decimal places as​ needed.)

Find the​ p-value.

​p-value = ______

​(Round to three decimal places as​ needed.)

State the conclusion.

( Do not reject / Reject ) H0. There is ( sufficient / insufficient ) evidence to conclude that the population mean waiting time is different from 3.6 minutes

Answer 1

Solution:

This is a two tailed test.

The null and alternative hypothesis is,

Ho: 3.6

Ha: 3.6

The test statistics,

t = ( - )/ (s/)

= ( 3.82 - 3.6 ) / ( 0.8 / 64 )

= 2.20

P- value = 0.031

The p-value is p =0.031 < 0.05, it is concluded that the null hypothesis is rejected.

Reject H0. There is sufficient evidence to conclude that the population mean waiting time is different from 3.6 minutes.