Question

The management at New Century Bank claims that the mean waiting time for all customers at its branches is less than that at the Public Bank, which is its main competitor. A business consulting firm took a sample of 200 customers from the New Century Bank and found that they waited an average of 4.5 minutes before being served. Another sample of 300 customers taken from the Public Bank showed that these customers waited an average of 4.75 minutes before being served. Assume that the standard deviations for the two populations are 1.2 and 1.5 minutes, respectively.

Test at the 2.5% significance level whether the claim of the management of the New Century Bank is true. Use and show the 5-step procedure.

Answer 1

we have given that

for New Century Bank

sample size=n1=200 sample mean=m1=4.5 SD1=1.2

for public bank

sample size =n2=300 sample mean =m2=4.75 SD2=1.5

consider New Century Bank as first sample and public bank as second sample

we need to test that New Century Bank have less waiting time than public bank so

now test statistics is given by

Since test is Left tailed so

P-Value =P(Z<-2.06)=0.02

since P-Value is less than level of significance so we reject H0 that is we have statistically significant evidence to conclude that New Century Bank management claim true.