A random sample of 81 credit sales in a department store showed an average sale of $68.00. From past data, it is known that the standard deviation of the population is $27.00. a. Determine the standard error of the mean. b. What is the 95% confidence interval of the population mean?

(a) Standard error of the mean is $5.97

(b) 95% confidence interval for the population mean is ($62.03, $73.97)

Step-by-step explanation:

(a) Error = t*sd/√n

sd = $27, n = 81, degree of freedom = n-1 = 81-1 = 80, t-value corresponding to 80 degrees of freedom and 95% confidence level = 1.990

Error = 1.990*$27/√81 = $5.97

(b) Confidence Interval = mean + or - error

Mean = $68

Error = $5.97

Lower bound = $68 - $5.97 = $62.03

Upper bound = $68 + $5.97 = $73.97

95% confidence interval is ($62.03, $73.97)