Question

You manage two call centers and are working on trying to reduce the amount of time customers are placed on hold. You believe the mean hold times at the two call centers are not the same so you start by testing the claim that the mean hold time for Call Center 1 is different than the mean hold time for Call Center 2 .

You wish to test the claim that the mean hold time for Call Center 1 is different than the mean hold time for Call Center 2 at a significance level of α = 0.002 α=0.002 . You obtain the following two samples of data from each center. Each data point is the amount of time (in seconds), a customer is placed on hold. Call Center 1 Call Center 2 64.2 65.8 58.6 66.6 61.5 61.9 56.5 70.9 78.6 61.2 67.5 54.3 46.5 46.8 55.4 47.1 70.4 61.9 75.9 52.7 53.5 36.6 50.2 54.0 57.7 41.7

What is the test statistic for this sample? test statistic = Round to 4 decimal places.

What is the p-value for this sample? p-value = Round to 4 decimal places.

The p-value is...

less than (or equal to) α α

greater than α α

This test statistic leads to a decision to...

reject the null

accept the null

fail to reject the null

As such, the final conclusion is that...

There is sufficient evidence to warrant rejection of the claim that the mean hold time for Call Center 1 is different than the mean hold time for Call Center 2.

There is not sufficient evidence to warrant rejection of the claim that the mean hold time for Call Center 1 is different than the mean hold time for Call Center 2.

The sample data support the claim that the mean hold time for Call Center 1 is different than the mean hold time for Call Center 2.

There is not sufficient sample evidence to support the claim that the mean hold time for Call Center 1 is different than the mean hold time for Call Center 2.

Answer 1

	Call center 1 ( X )		Call center 2 ( Y )
	64.2	8.5896	65.8	106.09
	58.6	7.1246	66.6	123.21
	61.5	0.0533	61.9	40.96
	56.5	22.7453	70.9	237.16
	78.6	300.3566	61.2	32.49
	67.5	38.8229	54.3	1.44
	46.5	218.1293	46.8	75.69
	55.4	34.4475	47.1	70.56
	70.4	83.3715	61.9	40.96
	75.9	214.0603	52.7	7.84
	53.5	60.3605	36.6	357.21
	50.2	122.5272	54	2.25
	57.7	12.7392	41.7	190.44
Total	796.5	1123.3278	721.5	1286.3

Mean

Standard deviation

Mean

Standard deviation

To Test :-

H0 :-  

H1 :-  

Test Statistic :-


t = 1.4679

Test Criteria :-
Reject null hypothesis if


DF = 23

| t | > t_{\alpha /2, DF} = 1.4679 < 3.485
Result :- Fail to Reject Null Hypothesis

Decision based on P value
P - value = P ( t > 1.4679 ) = 0.1557
Reject null hypothesis if P value < level of significance
P - value = 0.1557 > 0.002 ,hence we fail to reject null hypothesis
Conclusion :- We Accept H0

There is sufficient evidence to warrant rejection of the claim that the mean hold time for Call Center 1 is different than the mean hold time for Call Center 2.