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=0.001   

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
59.6 54.0 70.4 53.0 51.7 53.3 33.4 57.2 24.6 67.4 65.9 51.0 38.8 51.7 39.4	56.1 57.0 47.6 50.4 43.3 46.0 44.1 52.6 48.0 56.1 43.3

1. What is the test statistic for this sample?
   
   test statistic =  Round to 4 decimal places.
   
2. What is the p-value for this sample?
   
   p-value =  Round to 4 decimal places.
   
3. The p-value is...
   • less than (or equal to) αα
   • greater than αα
   
   
4. This test statistic leads to a decision to...
   • reject the null
   • accept the null
   • fail to reject the null
   
   
5. 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

The statistical software output for this problem is:

From above output:

Test statistic = 0.5260

p - Value = 0.6047

greater than α

Fail to reject the null

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.