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

a.

Sample size n= 242

Sample mean M = 1843.93

Sample standard deviation s= 516.42

Then 95% confidence interval of population mean is

=

t = t score for 95% confidence with df=n-1=241

= 1.97 ( from t table)

So the 95% confidence interval is

=

= (1843.93 65.398 )

= ( 1778.532 , 1909.328 )

b. the Claimed average sales of last year is 2120.55 usd . Clearly this is more than our 95% confidence interval of the mean sales.

So we have evidence that the company substantially overstate its average sales per invoice last year .