Q1. A normally distributed population has a mean of 40 and a standard deviation of 12. What does the central limit theorem say about the sampling distribution of the mean if samples of size 100 are drawn from this population?
a. In a random sample of 500 observations, we found the proportion of successes to be 48% Estimate with 95% confidence the population proportion of successes.
b. Repeat part (a) with n = 200
c. Repeat part (a) with n = 1000
d. Describe the effect on the confidence interval estimate of increasing the sample size.
Q2. The proportion of successes in a random sample of 400 was calculated as 50%.
a. Estimate the population proportion with 95% confidence.
b. Repeat part (a) with p = 33%
c. Repeat part (a) with p = 10%
d. Discuss the effect on the width of the confidence interval estimate of reducing the sample proportion.
Q3. A statistics practitioner working for MLB wants to supply radio and television commentators with interesting statistics. He observed several hundred games and counted the number of times a runner on first base attempted to steal second base. He found there were 373 such events, of which 259 were successful. Estimate with 95% confidence the proportion of all attempted thefts of second base that are successful.
Q4. A dean of a business school wanted to know whether the graduates of her school used a statistical inference technique during their first year of employment after graduations. She surveyed314 graduates and asked about the use of statistical techniques. After tallying the responses, she found that 204 used statistical inference within one year of graduation. Estimate with 90% confidence the proportion of all business school graduates who use their statistical education within a year of graduation.
Q5. What type of educational background do CEOs have? In one survey, 344 CEOs of medium and large companies were asked whether they had an MBA degree. There were 97 MBAs. Estimate with 95% confidence the proportion of all CEOs of medium and large companies who have MBAs.