Question: 7.1 A research group states that 16% of the firms of Type A increased their market research budgets in the past five years. For Type B firms, the figure was 9%.

(a) What are the mean and standard deviation of the sampling distribution of the difference between sample proportions, based on independent simple random samples of 100 firms of each type?

(b) What proportion of the sample differences \({{\hat{p}}_{A}}-{{\hat{p}}_{B}}\), would be between 0.05 and 0.10?

(c) Suppose that you took a simple random sample of size 100 from each industry. What is the probability that the difference you would observe would be equal to or less than 0.02?