Question

A sample of 64 account balances from a credit company showed an average daily balance of $1,040. The standard deviation of the population is known to be $200. We are interested in determining if the mean of all account balances (i.e., population mean) is significantly different from $1,000.

a.	Develop the appropriate hypotheses for this problem.
b.	Compute the test statistic.
c.	Compute the p-value.
d.	Using the p-value approach at 95% confidence, test the above hypotheses.
e.	Using the critical value approach at 95% confidence, test the hypotheses.

Answer 1

(A) we want to test whether the population mean is significantly different from 1000 or not

(B) Given that sample size n = 64, sample mean x bar = 1040, population standard deviation = 200 and population mean = 1000

z test statistic

(C) using z table, check 1.6 in the left most column and check 0.00 in the top row, then select the intersecting cell, we get

p value = 0.1096

(D) p value is greater than 0.05 significance level, so we failed to reject the null hypothesis

(E) z critical range for two sided test at 0.05 significance level or 95% confidence is -1.96 to 1.96. Calculated z statistic is between the critical range of z value, so we again failed to reject the null hypothesis