Suppose we are interested in the average net sales (in millions of dollars) for a population of 37 companies that manufacture computer equipment: (1) 42.88 (6) 253.20 (11) 18.99 (16) 90.48 (21) 6.58 (26) 7.30 (31) 29.50 (36) 21.13 (2) 43.36 (7) 103.19 (12) 30.90 (17) 17.33 (22) 8.75 (27) 4.59 (32) 20.52 (37) 29.83 (3 )9.08 (8) 2869.35 (13) 3009.49 (18) 7.96 (23) 39.98 (28) 6.03 (33) 8.43 (4) 40.94 (9) 196. 32 (14) 35.52 (19) 7.94 (24) 17.66 (29) 29.93 (34) 58.08 (5) 80.72 (10) 193.34 (15) 21.22 (20) 5.21 (25) 17.47 (30) 21.64 (35) 35.52

(a) Write and run a single R program that: i. calculates the average sales value for the population of 37 companies; ii. takes a simple random sample of these firms, of size n = 8, and, iii. calculates the average sales value for this sample.

(b) Repeat part (a) for three more samples. Considering the values of sales for the 37 companies in the population, explain why the sample averages take values less than 130, between 360 and 500, or between 735 and 850.

(c) Write and run another R program that: i. takes a unique random sample of n = 8 companies, and ii. uses the observations of the sample to derive an estimate of sales averages for all 37 companies, while giving an approximation the margin of error on the estimate of the mean, and a confidence interval of the average is about 95%. (Do not use functions from libraries.)