Question

Clearwater National Bank wants to compare the account checking practices by the customers at two of its branch banks – Cherry Grove Branch and Beechmont Branch. A random sample of 28 and 22 checking accounts is selected from these branches respectively. The sample statistics are shown on the next slide

Cherry Grove                                  Beechmont

n                                        28                                            22

x                                        $1025                                       $910

s                                         $150                                         $125

Let us develop a 99% confidence interval estimate of the difference between the population mean checking account balances at the two branch banks.

Please, show work.

Answer 1

We need to construct the 99% confidence interval for the difference between the population means μ1​−μ2​, for the case that the population standard deviations are not known. The following information has been provided about each of the samples:

Sample Mean 1	1025
Sample Standard Deviation 1	150
Sample Size 1	28
Sample Mean 2	910
Sample Standard Deviation 2	125
Sample Size 2	22

Based on the information provided, we assume that the population variances are equal, so then the number of degrees of freedom are df = n_1 + n_2 -2 = 28 + 22 - 2 = 48

The critical value for α=0.01 and df = 48 degrees of freedom is t_c = 2.682 . The corresponding confidence interval is computed as shown below:

Since the population variances are assumed to be equal, we need to compute the pooled standard deviation, as follows:

Since we assume that the population variances are equal, the standard error is computed as follows:

Now, we finally compute the confidence interval:

CI = (8.312, 221.688)