Question

A bank with a branch located in a commercial district of a city has the business objective of developing an improved process for serving customers during the noon-to-1 P.M. lunch period. Management decides to fist study the waiting time in the current process. The waiting time is defined as the number of minutes that elapses from when the customer enters the line until he or she reaches the teller window.

Data are collected from a random sample of 15 customers and stored in the Bank1 database.

For this sample: $7lMlm0X+wYNOFIUrIHqBQAAAABJRU5ErkJggg==$ = 4.2867, S₁ = 1.6379.

Suppose that another branch, located in a residential area, is also concerned with improving the process of serving customers in the noon-to-1 P.M. lunch period.

Data are collected from a random sample of 15 customers and stored in the Bank2 database.

For this sample: $0BwHTCKyoX7KoAAAAASUVORK5CYII=$ = 7.1146, S₂ = 2.0821.

1. 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 Critical Value approach with α = 0.05) In addition to equal variances, what other assumption is necessary to do this test?
2. If p-value = 0.000293 in (a), interpret its meaning.
3. Construct and interpret a 95% confidence interval estimate of the difference between the population means in the two branches?

Answer 1

Here wL hava S2 2-o8 2 2 Нурo theses: MI M2 Ho На: м, + Ma Test statisic 522-) 4.286-7.1146 (i5-1) x 6. 13 739-05-1{2os StIS-2 4.13435 {-4 .13 A 2005, df= 26 fertical value terito.05/ 2. 028 28 SinceSTT< -2.02P, we Aesact Ho support te su tcent eviden ce to Con cluяn: There claim and we can conciyde fna taese is di bheree bew een waitin o* be hwo branches At P valn- o. 00 o 2 93 b we resect Ho. Pvaln <0.05,

hie feveb margina) >tfmti can ce wi when the шy hy potheas be tne, Нe re abave ypomeca test . The gs seubt cient e don ce ot supрorting tne c lai m me a hs . cOn tid nce df 28 Дente to.os125 2.048 Now gsу X + Я,+ he2 4.2867-7.16)2.04/1S-1) X I. 637965-j) x2-082j 7 — 2о 8 279 1. 40 0 8 4- 2267 1.42 dоes not de tn tne abwe con conciude tnet nere is gs. confiden ce difterence и fi den ce nderve ,0, диз hеn e we Саn be tu pen tha populat тean hat there in tne to branches