Statistic

1. A retailer that sells home entertainment systems accumulated 10,451 sales invoices during the previous year.  The total of the sales amounts listed on the invoices (that is, the total sales claimed by the company) is $6,384,675 (or about $611 per sale on average).  In order to estimate the true total sales for the last year, an independent auditor randomly selects 350 of the invoices and determines the actual sales amounts by contracting purchasers.  The mean and standard deviation of the 350 sampled sales amounts are, sample mean (amount per sale) = $532, sample standard deviation = $168.

a) Find a 95% confidence level for M, the true mean sales amount per sales on the 10,451 invoices.
b) What does this interval say about the company's claim that the true total sales were $6,384,675?  Explain.

2. Suppose the federal government proposes to give a substantial tax break to automakers producing midsize cars that get a mean mileage of at least 31 mpg.  A sample of 49 midsize autos from a particular automaker resulted in an average of 31.5531 mpg and a standard deviation of 0.7992.  At the .05 level of significance, should this automaker be awarded the tax break?

3. Last year, television station WXYZ's share of the 10 p.m. news audience was approximately equal to, but no greater than, 25%.  The station's management believes (and would like to claim for advertising purposes) that the current share is higher than last year's 25 % share.  In an attempt to substantiate this claim, the station surveyed a random sample of 400 10 p.m. news viewers and found that 146 watched WXYZ 10 p.m. news.  At the .01 level of significance, do you believe the station's claim to be correct?