Question

According to the Stern Marketing Group, 9 out of 10 professional women say that financial planning is more important today than it was five years ago. Where do these women go for help in financial planning? Forty-seven percent use a financial advisor (broker, tax consultant, financial planner). Twenty-eight percent use written sources such as magazines, books, and newspapers. Suppose these figures were obtained by taking a sample of 530 professional women who said that financial planning is more important today than it was five years ago. a. Construct a 95% confidence interval for the proportion of professional women who use a financial advisor. Use the percentage given in this problem as the point estimate. b. Construct a 90% confidence interval for the proportion of professional women who use written sources. Use the percentage given in this problem as the point estimate.

(Round your answers to 4 decimal places.)

Answer 1

a)
sample proportion, = 0.47
sample size, n = 530
Standard error, SE = sqrt(pcap * (1 - pcap)/n)
SE = sqrt(0.47 * (1 - 0.47)/530) = 0.0217

Given CI level is 95%, hence α = 1 - 0.95 = 0.05
α/2 = 0.05/2 = 0.025, Zc = Z(α/2) = 1.96

CI = (pcap - z*SE, pcap + z*SE)
CI = (0.47 - 1.96 * 0.0217 , 0.47 + 1.96 * 0.0217)
CI = (0.4275 , 0.5125)

b)
sample proportion, = 0.28
sample size, n = 530
Standard error, SE = sqrt(pcap * (1 - pcap)/n)
SE = sqrt(0.28 * (1 - 0.28)/530) = 0.0195

Given CI level is 90%, hence α = 1 - 0.9 = 0.1
α/2 = 0.1/2 = 0.05, Zc = Z(α/2) = 1.64

CI = (pcap - z*SE, pcap + z*SE)
CI = (0.28 - 1.64 * 0.0195 , 0.28 + 1.64 * 0.0195)
CI = (0.2480 , 0.3120)