8. 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)
Sampling error and calculation of chi-square statistic as shown in the solution.