Question

A local bank needs information concerning the account balance of its customers. A random sample of 15 accounts was checked. The mean balance was $686.75 with a standard deviation of $256.20.

A. Construct a 98% confidence interval for the population mean, assuming account balances are normally distributed.

B. Based on your previous answer, would a population mean of $500 be unusual? What about a mean of $800?

Answer 1

Solution:

Given:

n = sample size = 15

Sample mean =

Sample Standard Deviation = s = 256.20

Part A) Construct a 98% confidence interval for the population mean

Formula:

where

t_c is t critical value for c = 98% confidence level.

Thus two tail area = 1 - c = 1 - 0.98 = 0.02

and

df = n - 1 =  15 - 1 = 14

t_c = 2.624

Thus

Thus

Thus  a 98% confidence interval for the population mean  account balance of customers is between $513.17 to $860.33.

Part B) Based on your previous answer, would a population mean of $500 be unusual? What about a mean of $800?

Since $500 < lower limit of confidence interval , a population mean of $500 would be unusual

and $800 is within the limits of confidence interval , a population mean of $500 would be usual.