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

Given Population Mean =   = 2120.55

Sample size = n = 242

Sample Mean = = 1843.93

Sample Standard Deviation = s = 516.42

(a) Given Confidence Interval = 95%

So = 5% = 0.05

Therefore

Now  

.

Therefore 95% Confidence Interval of is

Therefore the 95% Confivdence Interval of Population is

(b) Actually the company claimed that the average sales amount per invoice was µ = 2120.55 USD

But in the calculation of 95% confidence interval we got

Based on above computed 95%  confidence interval the company substantially overstated its average sales per invoice last year