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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 3.8 minutes. You select a random sample of 81 orders. The sample mean waiting time is 3.92 minutes, with a sample standard deviation of 0.9 minute. Complete parts (a) and (b) below.

a. At the 0.10 level of significance, is there evidence that the mean waiting time is different from 3.8 minutes? Choose the correct null and alternative hypotheses to decide this:

Determine the test statistic.

Find the p-value.

State the conclusion.

Presenting step by step solution for this problem. 

The population mu = 3.8 minutes.

The sample statistics are: x_bar = 3.92, standard deviation = 0.9, n = 81. 

This is a two-tailed test of hypothesis, 


Ho:  mu  = 3.8 minutes

Ha: mu != 3.8 minutes. (Not equal to),

Remeber the t-statistic formula:  t = (x_bar  - mu)/(s/sqrt(n))

t statistic = (3.92 - 3.8)/0.9/sqrt(81) =  1.2

Remember that the p value for any statistic can be obtained using Excel.  Because it is a two-tailed test, the function  =T.DIST.2T(1.2,80) is appropriate. 

 =T.DIST.2T(1.2,80)  = 0.2337. 

Conclusion: Do not reject the null hypothesis. 



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