Question

According to Thomson Financial, through January 25, 2006, the majority of companies reporting profits had beaten estimates (BusinessWeek, February 6, 2006). A sample of 262 companies showed 204 beat estimates, 29 matched estimates, and 29 fell short. a) Determine the margin of error and provide a 90% confidence interval for the proportion that beat estimates. b) How large a sample is needed if the desired margin of error is .10?

Answer 1

a) We know, ~ N(0,1)

The 90% confidence interval of the proportion that beat estimates =

[, ], where, = 204/262 = 0.7786, n = 262

Thus, 90% C.I. = [0.7786 - 0.0421, 0.7786 + 0.0421] = [0.7365, 0.8207]

b) Let the required sample size be n for margin of error of 0.1

Thus, = 0.1 assuming = 0.7786 as obtained before

Hence, n = 47 (approximately).