{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Chapter 12

# Chapter 12 - 6851F_ch12_189_193 20:05 Page 189 12 12.1(a...

This preview shows pages 1–3. Sign up to view the full content.

189 12 12.1 (a) Population: the 175 residents of Tonya’s dorm; p is the proportion who like the food. (b) ± 0.28. 12.2 (a) The population is the 2400 students at Glen’s college, and p is the proportion who believe tuition is too high. (b) ± 0.76. 12.3 (a) The population is the 15,000 alumni, and p is the proportion who support the president’s decision. (b) ± 0.38. 12.4 (a) No—the population is not large enough relative to the sample. (b) Yes—we have an SRS, the population is 48 times as large as the sample, and the success count (38) and failure count (12) are both greater than 10. (c) No—there were only 5 or 6 “successes” in the sample. 12.5 (a) No— np 0 and n (1 ² p 0 ) are less than 10 (they both equal 5). (b) No—the expected number of failures is less than 10 ( n (1 ² p 0 ) ± 2). (c) Yes—we have an SRS, the population is more than 10 times as large as the sample, and np 0 ± n (1 ² p 0 ) ± 10. 12.6 (a) so the 95% confidence interval is 0.54 ³ (1.96)(0.01561) ± 0.51 to 0.57. The margin of error is about 3%, as stated. (b) We weren’t given sample sizes for each gender. (However, students who know enough algebra can get a good estimate of those numbers by solving the system x ´ y ± 1019 and 0.65 x ´ 0.43 y ± 550: approximately 508 men and 511 women.) (c) The margin of error for women alone would be greater than 0.03 since the sample size is smaller. 12.7 (a) The methods can be used here, since we assume we have an SRS from a large population, and all relevant counts are more than 10. For TVs in rooms: and ± so the 95% confidence interval is to 0.689. For preferring Fox: and ± so the 95% confidence interval is to 0.203. (b) In both cases, the margin of error for a 95% confidence interval (“19 cases out of 20”) was (no more than) 3%. (c) We test H 0 : p ± 0.5 versus H a p µ 0.5. The test statistic is which gives very strong evidence against H 0 ( P 0.0002); we conclude that more than half of teenagers have TVs in their rooms. (Additionally, the interval from (a) does not include 0.50 or less.) With the TI-83, z ± 10.379 and P ± 1.577 · 10 ² 25 . 12.8 (a) and since and are both greater than 10, the confidence interval based on z can be used. The 95% confidence interval for p is or 0.59435 to 0.72565. .66 ³ 1 1.96 2 1 11 .66 21 .34 2> 200 2 ± .66 ³ 0.06565, n 1 1 ² ˆ p 2 ± 68 n ˆ p ± 132 ˆ p ± .66, z ± 1 0.66 ² 0.50 3 1 0.5 0.5 2 1048 ± 10.36, 0.18 ³ 1 1.96 0.01187 2 ± 0.157 0.01187, SE p ˆ ± 2 1 0.18 0.82 1048 ˆ p 2 ± 0.18 ± 0.631 0.66 ³ 1 1.96 0.01463 2 2 1 0.66 0.34 1048 ± 0.01463, SE p ˆ ˆ p 1 ± 0.66 SE p ˆ ± 2 1 0.54 0.46 1019 ± 0.01561, ˆ p ˆ p ˆ p 6851F_ch12_189_193 17/9/02 20:05 Page 189

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
190 Chapter 12 (b) Yes; the 95% confidence interval contains only values that are less than 0.73, so it is likely that for this particular population, p differs from 0.73 (specifically, is less than 0.73). 12.9 (a) and (b) Checking conditions, and are both at least 10. Provided that there are at least (84) ( p ) = 840 applicants in the population of interest, we are safe constructing the confidence inerval. 0.1098 to 0.2473. 12.10 —use n 5 356. With so the true mar- gin of error is (1.645)(0.0265) 5 0.0436.
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 5

Chapter 12 - 6851F_ch12_189_193 20:05 Page 189 12 12.1(a...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online