A chartered bank is experimenting with a new method of servi

A chartered bank is experimenting with a new method of serving its customers over the lunch hour peak period, with the aim of reducing customer wait times. The table below describes the waiting times for two of the bank\'s branches. The times shown for Bank 1 are observed under the \"old method\" of serving customers, while the times shown for Bank 2 are observed under the \"new method\" of serving customers. Using the pooled estimate of the standard deviation of 1.8733, conduct the appropriate test of hypothesis to determine if the new method significantly reduces waiting times. Use a 1% level of significance. Keep your work to 4 decimals.

Solution

First create null and alternate as

H0: Mean 1 = Mean 2

Ha: Mean 1>mean 2

Right tailed test

Mean 1 - Mean 2 = 2.828

Std error for difference = 1.733

t statistic = 1.632

df = 15+15-2 = 28

p value = 0.1139

As p >0.01, the difference is not much significant

Accept null hypothesis

Waiting time has not reduced significantly

Group	Group One	Group Two
Mean	7.11500	4.28700
SD	2.08200	6.38000
SEM	0.53757	1.64731
N	15	15