According to the survey of 50 enterpreneurs, which were randomly selected across the industry, only 20 expect an improvement of the economic conditions in the course of next year, and the others have pessimistic expectations. (a) What is the sample proportion of enterpreneurs who are pessimistic about the economic conditions next year? (b) Can the Central Limit Theorem be applied for p-p? Discuss the validity of both conditions. (c) Find the approximate standard error, SE,, using p estimated from the sample. (d) Construct the 95% confidence interval for the proportion of pessimistic expectations in popu- lation, p. (e) Does the confidence interval provide a strong evidence that p > 0.5? Explain. (f) Assuming does not change, what is a minimum sample size n is needed for the width of the 95% confidence interval be less than 0.1?