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. Appendix A Statistical Tables (Round your answers to 4 decimal places.)

a. ______≤ p ≤______

b. _______≤ p ≤_______

Answer 1

Solution :

Given that,

n = 530

Point estimate = sample proportion = = 0.47

1 - = 1 - 0.47 = 0.53

At 95% confidence level

= 1 - 95%

=1 - 0.95 =0.05

/2 = 0.025

Z/2 = Z_{0.025 = 1.960}

Margin of error = E = Z _{/ 2} * (( * (1 - )) / n)

= 1.96 (((0.47 * 0.53) / 530)

= 0.0425

A 95% confidence interval for population proportion p is ,

- E p + E

0.47 - 0.0425 p 0.47 + 0.0425

0.4275 p 0.5125

( 42.75% p 51.25% )

b) Given that,

n = 530

Point estimate = sample proportion = = 0.28

1 - = 1 - 0.28 = 0.72

At 90% confidence level

= 1 - 90%

=1 - 0.90 =0.10

/2 = 0.05

Z/2 = Z_{0.05 = 1.645}

Margin of error = E = Z _{/ 2} * (( * (1 - )) / n)

= 1.645 (((0.28 * 0.72) /530 )

= 0.0357

A 90% confidence interval for population proportion p is ,

- E p + E

0.28 - 0.0357 p 0.28 + 0.0357

0.2443 p 0.3157

( 24.43% p 31.57% )