The president of Amalgamated Retailers International, Samiha Peterson, has asked for your assistance in studying the market penetration for the company's new cell phone. You are asked to determine two markets and determine if the market share is equal to the company's claim of 35%. You obtain a random sample of potential customers from each area. The sample indicates that 258 out of a total sample of 800 indicates they will purchase from Amalgamated.

[a] Using a probability of error 0.03, test the hypothesis that the market shares equals the company's claim of 35% versus the hypothesis that the market share is not equal to the company's claim.

[b] Using a probability of error 0.03, test the hypothesis that the market shares equals the company's claim of 35% versus the hypothesis that the market share is less than the company's claim.

For each answer the following questions:

1. Problem statement
2. Assumptions
3. Null Hypothesis, Alternative Hypothesis
4. The significance level
5. Test statistic (as an equation)
6. Decision rules
7. JMP output
8. Interpretation