Question

1. margin of error: 0.04; confidence level: 99%; from a prior study, $hat{p}$ is estimated by 0.12. a) 254 b) 526 c) 18 d) 438

solve the problem. round the point estimate to the nearest thousandth.

1. 32 randomly picked people were asked if they rented or owned their own home, 8 said they rented. obtain a point estimate of the proportion of homeowners. a) 0.750 b) 0.781 c) 0.250 d) 0.200
2. 50 people are selected randomly from a certain population and it is found that 12 people in the sample are over 6 feet tall. what is the point estimate of the proportion of people in the population who are over 6 feet tall? a) 0.76 b) 0.24 c) 0.18 d) 0.50

use the given degree of confidence and sample data to construct a confidence interval for the population proportion

1. n = 85, x = 49; 98% confidence a) 0.451 < p < 0.701 b) 0.471 < p < 0.681 c) 0.470 < p < 0.682 d) 0.450 < p < 0.702
2. n = 130, x = 69; 90% confidence a) 0.461 < p < 0.601 b) 0.463 < p < 0.599 c) 0.459 < p < 0.603 d) 0.458 < p < 0.604
3. of 346 items tested, 12 are found to be defective. construct the 98% confidence interval for the proportion of all such items that are defective. a) 0.0110 < p < 0.0584 b) 0.0154 < p < 0.0540 c) 0.0118 < p < 0.0576 d) 0.0345 < p < 0.0349
4. when 328 college students are randomly selected and surveyed, it is found that 122 own a car. find a 99% confidence interval for the true proportion of all college students who own a car. a) 0.320 < p < 0.424 b) 0.310 < p < 0.434 c) 0.303 < p < 0.441 d) 0.328 < p < 0.416
5. of 380 randomly selected medical students, 21 said that they planned to work in a rural community. find a 95% confidence interval for the true proportion of all medical students who plan to work in a rural community. a) 0.0280 < p < 0.0826 b) 0.0251 < p < 0.0854 c) 0.0360 < p < 0.0745 d) 0.0323 < p < 0.0782
6. a study involves 607 randomly selected deaths, with 35 of them caused by accidents. construct a 98% confidence interval for the true percentage of all deaths that are caused by accidents. a) 3.56% < p < 7.97% b) 3.91% < p < 7.62% c) 3.33% < p < 8.21% d) 4.20% < p < 7.33%
7. of 260 employees selected randomly from one company, 18.46% of them commute by carpooling. construct a 90% confidence interval for the true percentage of all employees of the company who carpool. a) 14.5% < p < 22.4% b) 12.3% < p < 24.7% c) 12.9% < p < 24.1% d) 13.7% < p < 23.2%

Explanation:

Answer:

(12) A. 254
(13) A. 0.750
(14) B. 0.24
(15) C. \(0.470 < p < 0.682\)
(16) A. \(0.461 < p < 0.601\)
(17) C. \(0.0118 < p < 0.0576\)
(18) C. \(0.303 < p < 0.441\)
(19) A. \(0.0280 < p < 0.0826\)
(20) B. \(3.91\% < p < 7.62\%\)
(21) A. \(14.5\% < p < 22.4\%\)