Moon Shine Company is a medium-sized manufacturer of shampoo. During the past years the company has increased the number of product Variations of Moon-Shine shampoo that are available from three to five to increase their market share, Management conducted a survey to compare sales of Moon Shine shampoo with sales of Sun Shine and Star Shine, their two major competitors. A sample of 1,800 housewives indicated the following frequencies with respect to most recent shampoo purchased

Shampoo Total Number Buying

1. Moon Shine 425

2. Sun Shine 1175

3. Star Shine 200

Total 1800

Past experience had indicated that three times as many households preferred Sun Shine to Moon Shine and that in turn twice as many households preferred Moon Shine to Star Shine. Management wants to determine if the historic tendency still holds, given Moon Shine Company has increased the range of shampoos available.

(a) State the null and alternate hypotheses.

(b) How many degrees of freedom are there?

(c) What is the chi-square critical table value at the 5

percent level?

(d) What is the calculated x? value? Show all your

calculations.

(e) Should the 'null hypothesis be rejected or not? Explain.