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

Since , the population standard deviation is not known.

Therefore , use t-distribution.

Now , df=degrees of freedom=n-1=242-1=241

The critical value is , ; The Excel function is , =TINV(0.05,241)

The 95% confidence interval for the mean sales amount per invoice is ,

Now , the null and alternative hypothesis is ,

Decision : Here , the value 2120.55 does not lies in the rejection region.

Therefore , reject Ho.

b) Based on this confidence interval, the company substantially overstate its average sales per invoice last year