A bank branch located in a commercial district of a city has developed an improv

Question

A bank branch located in a commercial district of a city has developed an improved process for serving customers during the noon to 1 pm lunch period. The waiting time (defined as the time from when customers join the line until they reach the teller's window) of all customers during this hour is recorded over a period of one week. A random sample of 15 customers is selected, and the results are as follows: 4.21 5.55 3.02 5.13 4.77 2.34 3.54 3.20 4.50 6.10 0.38 5.12 6.46 6.19 3.79 a. At the 0.05 level of significance, is there evidence that the mean waiting time is less than 5 minutes? b. What assumption must hold in order to perform the test in (a)? c. Evaluate this assumption through a graphical approach. Discuss. d. As a customer walks into the branch office during the lunch hour, she asks the branch manager how long she can expect to wait. The branch manager replies, 'Almost certainly not longer than 5 minutes.' On the basis of the results of (a), evaluate this statement.

Explanation / Answer

Here as the sample size is less than 30 , we have to apply t test for single population.

X/n = Xbar = sample mean = 64.3/15 = 4.2867

37.56193335

s square=sample mean square = (X-Xbar)square/n-1=37.5619/14=2.683 ,s = 1.638

To test,

vs

µ0 = 5 minutes

Under H0, test statistic is, t = [Xbar - mu0]/s/square root n

= [4.2867-5]/(1.638/3.873)

= -1.6866

It is a left sided test , Hence critical region is given by ,

C={t<-talpha} now , t alpha = t tab at 14 degrees of freedom & 5% level of significance is 1.761

Here, tcal = -1.6866 ,

-talpha = -t tab = -1.761

As aresult calculated test statistic does not lie in the critical region That is t cal is not less than -ttab. Therefore we accept HO.

Hence, mu = mu0 = 5 minutes.

There is no any evidence that mean waiting time is less than 5 minutes.

Assumption : samples are come from normal population with unknown variance. As well sample size is less than 30, then we apply t test.

Branch manager's reply that almost not more than 5 minutes is correct.As mu mu0 = 5 minutes = statement of null hypothesis which is accepted.

X 4.21 5.55 3.02 5.13 4.77 2.34 3.54 3.2 4.5 6.1 0.38 5.12 6.46 6.19 3.79 64.3

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