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A company that has many department stores in the Southern states wanted to find at two such stores the percentage of sales for which at least one of the items was returned. A sample of 800 sales randomly selected from store A showed that for 240 of them at least one item was returned. Another sample of 900 sales randomly selected from store B showed that for 279 of them at least one item was returned.
a) Construct a 98% confidence interval for the difference between the proportions of all sales at the two stores for which at least one item is returned.
b) Using 1% significance level, can you conclude that the two stores proportions of all sales for which at least one item is returned are different?
c) Find the p-value for the test mentioned in part b.

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How to model player movement using First Order Logic, in a game environment.

Prove that for h sufficiently small, iterative use of a corrector formula does produce a convergent sequence and that the limit of this sequence is the unique value Y_(k+1) satisfying the corrector formula.

a company manufactures three product X,Y and Z. the sales volume for X is at least 50% of the total sales of all three products. however, the company cannot sell more than 80 units of X per day. the three products use one raw material, of which the maximum daily availability is 240 lb. the usage rates of the material are 2 lb per unit of X, 4 lb per unit of Y and 3 lb per unit of Z. the unit prices for X,Y and Z are $20, $50 and $35 respectively.
a) formulate a mathematical model for the problems
b) determine the optimal mix for the company

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Rhonda Brennan found her first job after graduating from college through the classifieds of the Miami Herald. She was delighted when the offer came through at $16.70 per hour. She completed her W-4 stating that she is married with a child and claims an allowance of 1. Her company will pay her biweekly for 80 hours (assume a tax rate of 6.2% on $106,800 for Social Security and 1.45% for Medicare).

Calculate her take-home pay for her first check.