Question

A company sells and installs satellite dishes and receivers for both private individuals and commercial establishments. The company accumulated a total of N = 2418 sales invoices last year. The company claims that the average sales amount per invoice was µ = 2120.55 USD. In order to verify that claim, an independent auditor randomly selects n = 242 of the invoices and determines the actual sales amounts by contacting the purchasers. When the sales amounts are averaged, the mean of the actual sales amounts for the 242 sampled invoices is x = 1843.93, while the sample standard deviation is s = 516.42.. a) Construct a 95% confidence interval for the the mean sales amount per invoice. b) Based on this confidence interval did the company substantially overstate its average sales per invoice last year?

Answer 1

n=242

Sample mean

The standard deviation of sample is

Answer(a):

The 95% confidence interval of mean sales amount per invoice is given by

Lower limit= 1778.537

Upper limit = 1909.323

Answer(b):

From above confidence interval we are 95% confident that the mean sales amount per invoice is between 1778.537 and 1909.323 and this confidence interval does not include the claimed value by company (i.e. $2120.55). So based on above evidence we can say that the company substantially overstate its average sales per invoice last year