Question

1. 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 630 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.)

2. The highway department wants to estimate the proportion of vehicles on Interstate 25 between the hours of midnight and 5:00 A.M. that are 18-wheel tractor trailers. The estimate will be used to determine highway repair and construction considerations and in highway patrol planning. Suppose researchers for the highway department counted vehicles at different locations on the interstate for several nights during this time period. Of the 3,633 vehicles counted, 845 were 18-wheelers.

a. Determine the point estimate for the proportion of vehicles traveling Interstate 25 during this time period that are 18-wheelers.
b. Construct a 99% confidence interval for the proportion of vehicles on Interstate 25 during this time period that are 18-wheelers.

(Round your answers to 3 decimal places.)

Answer 1

Answer:

1.

a) Given,

sample proportion p^ = 0.47

sample n = 630

Here at 95% CI, z value is 1.96

CI = p^ +/- z*sqrt(p^(1-p^)/n)

substitute values

= 0.47 +/- 1.96*sqrt(0.47(1-0.47)/630)

= 0.47 +/- 0.039

= (0.4310 , 0.5090)

b) At 90% CI , z value is 1.645

CI = p^ +/- z*sqrt(p^(1-p^)/n)

substitute values

= 0.28 +/- 1.96*sqrt(0.28(1-0.28)/630)

= 0.28 +/- 0.0351

= (0.2449 , 0.3151)

2a)

Point estimate = x/n = 845/3633 = 0.2326

b)

Here at 99% CI, z value is 2.58

CI = p^ +/- z*sqrt(p^(1-p^)/n)

substitute values

= 0.2326 +/- 2.58*sqrt(0.2326(1-0.2326)/3633)

= 0.2326 +/- 0.0181

= (0.215 , 0.251)