1. A random sample of nine CEOs reported how many times per year they play tennis (Table 1). Assuming the number of games played is normally distributed and the population standard deviation σ = 12. Based on these data (if you want to run R, please use ceo.csv posted on Canvas),
Table 1 Observation 1 2 3 4 5 6 7 8 9
Plays 24 41 60 32 52 19 45 31 38
(a) Give a margin of error of 95% confidence (Round it to two decimal places)
(b) What is a 95% confidence interval for µ? (Clearly provide your lower and upper limits)
(c) Explain in simple terms the meaning of the 95%.
(d) If you wanted 99% confidence for the same study, would your margin of error be greater than, equal to, or less than? What about the confidence interval? Explain your answer. (Without calculation, you can answer it).
(e) What is a 95% confidence interval for µ if the sample size changes to 100? Is it wider than, equal to, or narrower than that of the sample size of 9. Explain your answer. (Without calculation, you can answer it).