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 study two markets and determine if the difference in market share remains the same. Historically, in market 1 in western Poland, Amalgamated has had a 30% market share. Similarly, in market 2 in southern Austria, Amalgamated has had a 35% market share. You obtain a random sample of potential customers from each area. From market 1, 258 out of a total sample of 800 indicate they will purchase from Amalgamated. From market 2, 260 out of 700 indicate they will purchase from Amalgamated.
[a] Using a probability of error α=0.03, test the hypothesis that the market shares are equal versus the hypothesis that they are not equal (market 2 - market 1).
[b] Using a probability of error α=0.03, test the hypothesis that the market shares are equal versus the hypothesis that the share in market 2 is larger.
I need to include the following in my answer:
1. The problem statement
2. Assumptions
3. The null and alternate hypothesis statements
4. The significance level
5. The test statistic
6. Decision Rules
7. Calculate Test Statistic and find the p-value
8. Interpret the results of the test.