Question

ls The Bunk of New England is concerned about the amount of debt being accrued by customers using its credit cards. The Board of directors decided to install an expensive monitoring system if the mean for all of the bank's customers is greater than $2000. The bank randomly selected 100 credit card holders and determined the amounts they charged. For this sample group the mean is S2177 and standard deviation is $843. Use 025 level of significance to test the claim that the mean amount charged is greater han $2000 Based on the results of testing, will the monitoring system be implemented? points).

Answer 1

Let denotes the mean amount charged for all of the bank's customers.

To test against
H1 : μ > 2000

Here

sample mean

sample standard deviation

s 843

and sample size

The test statistic can be written as

which under H₀ follows a t distribution with n-1 df.

We reject H₀ at 2.5% level of significance if p-value < 0.025

Now,

The value of the test statistic

and P-value

Since P-value < 0.025, so we  reject H₀ at 2.5% level of significance and we can conclude that the mean amount charged is significantly greater than $2000