1. A telephone survey utilized a sampling frame of 2000 numbers, and had a response rate of 25%. A question asked respondents if they preferred Brand 1, Brand 2, or Brand 3. According to the company, 35% of their customers preferred Brand 1, 35% preferred Brand 2, and 30% preferred Brand 3. The telephone survey found that 40% preferred Brand 1, 30% preferred Brand 2, and the remainder preferred Brand 3.

a) What is the sampling error of this sample?

b) Is the company's assumption about their customers' preferences validated by the study? (show all the calculations)

2. An IQ test supposedly measures intelligence. The theoretical distribution of IQ has a mean of 100 and a standard deviation of 15. An entrepreneur believes that people who prefer environmentally safe products are more intelligent than people who do not. He wishes to be 95% sure of his estimate of the average intelligence if he finds customers who buy environmentally safe products are only two points higher than average. Design a study for this businessman.

a) What is your operational definition of intelligence?

b) Who is your population?

c) How will you select a sample?

d) How many people will you sample?