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Bank A and Bank B have each developed an improved process for serving customers. The waiting period from the moment a customer enters until he or she reaches the counter needs to be shortened. A random sample of 10 customers is selected from each bank and the results (in minutes) are shown in the accompanying data table. Complete parts (a) through (d).

a. Assuming that the population variances from both banks are equal, is there evidence of a difference in the mean waiting time between the two branches? (Use a=0.1.)

Bank A Bank B
2.67 3.01
2.36 4.09
3.13 4.02
3.03 5.77
3.79 5.92
4.81 6.71
4.82 6.97
4.88 7.15
5.18 7.51
5.24 10.71

Find the test statistic

Test statistic

 

There are different applications that you can use to calculate the sample statistics, 

WiFi only

mean = 38.8

Standard deviation = 10.932


4G/WiFi

Mean = 48.1

Standard deviation = 12.706

Use statistics from your samples and replace in the formulas below. 

Pooled standard deviation calculation, 

s^2  = (n1-1 * s1^2   + n2-1 * s2^2)/(n1 + n2  - 2)

s^2  = (n1-1 * s1^2   + n2-1 * s2^2)/(n1 + n2  - 2)

s^2  = (9 * 10.932^2 + 9 * 12.706^2)/(10+10-2)

s^2 = 140.48


t statistic  = (38.8 - 48.1)/sqrt(140.48 * (1/10 + 1/10)) = -1.755


pooled variances used


 

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