Question

Banks once had a separate customer waiting line for each teller window. Numerous banks have now gone to a single waiting line that feeds the teller windows as vacancies occur. For one bank a simple random sample of wait time (in minutes) using the single waiting line was taken and the results are below: 6.5 6.6 6.7 6.8 7.1 7.3 7.4 7.7 7.7 7.7 The mean wait time for multiple lines was 7.5 minutes and the known standard deviation was 1.8 minutes. Determine whether the new single line system is better than the old system. That is test the hypothesis that the new single line system is less than the mean of the old system. Discuss your results. Whether you reject your null hypothesis or not, are there other reasons to go to a single line system? Discuss.

Answer 1

using excel>addin>phstat>one smaple test

we have

Z Test of Hypothesis for the Mean
Data
Null Hypothesis                       m=	7.5
Level of Significance	0.05
Population Standard Deviation	1.8
Sample Size	10
Sample Mean	7.15
Intermediate Calculations
Standard Error of the Mean	0.5692
Z Test Statistic	-0.6149
lower-Tail Test
Upper Critical Value	-1.6449
p-Value	0.2693
Do not reject the null hypothesis

the null and alternative hypothesis is

Ho:u=7.5

Ha:u>7.5 (one tailed )

the value of test stat z =-0.6149

p value is 0.2693 since p value is greater than 0.05 so we reject Ho and conclude that new single line system is not less than the mean of the old system