# a4s - than 1.96 Question 3 We have n = 40 ¯ x = 2 31,s = 6...

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MATH 1131 3.0 - Fal 2010 Solution for Assignment 4 Question 1: It is given that n = 2815 ,x = 1885 and hence ˆ p = 0 . 6696 a. the required CI is 0 . 6696 ± 1 . 82 q 0 . 6696(1 - 0 . 6696) / 2815 (0 . 6531 , 0 . 6861). b. The margin of error is 0.0165. Based on the data, with 93.15% conﬁdence, the diFerence between the estimated pro- portion and the population proportion of people in favour of the death penalty for convicted murderer is 1.65%. c. 1 . 645 q 0 . 5(1 - 0 . 5) /n 0 . 02 n 41 . 125. Therefore need at least 1692 people. Question 2: a. Based on the provided information, the side-by-side boxplot can be obtained. Since the boxes overlapped, there does not seem to have a diFerence between male and female. b. Since both sample sizes are large, we can apply CLT and the required CI for μ F - μ M is (2 . 99 - 2 . 86) ± 1 . 96 q 2 . 34 2 / 1117 + 2 . 22 2 / 870 ( - 0 . 07 , 0 . 33). c. Since 0 is the the 95% CI of part (b), with 95% conﬁdence, no signiﬁcant diFerence between the mean time spent on social computer networrk of the 2 sexes. d. As stated in (a), we applied CLT. e. 99% CI will be longer than the 95% CI because the table value you use is 2.575 rather
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Unformatted text preview: than 1.96. Question 3: We have n = 40 , ¯ x = 2 . 31 ,s = 6 . 92. a. The required CI is 2 . 31 ± 2 . 575 6 . 92 √ 40 ⇔ (-. 51 , 5 . 13). b. Based on the given data, with 99% conﬁdence, the mean gain in weight is between losing 0.51 pounds to gaining 5.13 pounds. c. Since 0 is in the 99% CI, with 99% conﬁdence, the program is not eFective. d. The width of the 95% CI is 2(1 . 96) 6 . 92 √ 40 = 4 . 2891. Question 4: Let X be the placebo and Y be the aspirin group. Then n = 684 ,x = 28 ,m = 676 ,y = 18 and also ˆ p X = 0 . 0409 , ˆ p Y = 0 . 0266. a. The required CI for p X-p Y is (0 . 0409-. 0266) ± 1 . 96 q . 0409(1-. 0409) / 684 + 0 . 0266(1-. 0266) / 676 ⇔ (-. 0049 , . 0335) b. With 95% conﬁdence, the diFerence is 0.59% (asiprin higher) to 4.45% (placebo higher). c. Since 0 is in the 95% CI, no evidence that aspirin treatment is eFective....
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