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

Soluiton-A:

n=242

xbar=1843

s=516.42

alpha=0.05

alpha/2=0.05/2=0.025

df=n-2=242-1=241

t critical in excel=

=T.INV(0.025,241)

=1.969856213

95% confidence interval for mean sales amount per invoice.

=xbar-t*s/sqrt(n),xbar+t*s/sqrt(n)

1843-1.969856213*516.42/sqrt(242),1843+1.969856213*516.42/sqrt(242)

1777.607,1908.393

we are 95% confident that the true mean sales amount per invoice lies in between  1777.607 and 1908.393

Solution-b:

Ho:Mu=2120.55

Ha:Mu not =2120.55

since mu =2120 55 is not in the interval

Reject Ho

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