stat101-hw9-solution

stat101-hw9-solution - Julie Tung and Wei Professor Rakhlin...

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Julie, Tung and Wei Professor Rakhlin STAT 101 HW9 Solutions December 9, 2011 64 points in total Question. Chap 15, # 46 (5 points) Show the 95% z-interval or t-interval for the indicated parameter. (a) (1 point) μ given ¯ x = - 45 , s = 80 , n = 33 ¯ x ± t 0 . 05 / 2 s n = - 45 ± t 0 . 05 / 2 80 33 which turns out to be -73.36677 and -16.63323. (1 point, 0.5 for some work, 0.5 for the correct answer. Reasonable rounding suffice) (b) (1 point) μ given ¯ x = 255 , s = 16 , n = 21 ¯ x ± t 0 . 05 / 2 s n = 255 ± t 0 . 05 / 2 16 21 which turns out to be 247.8881 and 262.1119 (1 point, 0.5 for some work, 0.5 for the correct answer. Reasonable rounding suffice) (c) (1 point) p given ˆ p = 0 . 25 , n = 48 ˆ p ± z 0 . 05 / 2 ˆ p (1 - ˆ p ) n = 0 . 25 ± z 0 . 05 / 2 0 . 25(1 - 0 . 25) 48 which turns out to be 0.1275023 and 0.3724977 (1 point, 0.5 for some work, 0.5 for the correct answer. Reasonable rounding suffice) (d) (2 point) p given ˆ p = 0 . 9 , n = 52 We must compute Wilson’s intervals because (1 - ˆ p )52 = 5 . 2 < 10 (1 point). Therefore, the intervals are ˆ p 0 ± z 0 . 05 / 2 ˆ p 0 (1 - ˆ p 0 ) n +4 where ˆ p 0 = 52(0 . 9)+2 52+4 = 0 . 8714286. Then, our interval becomes 0.7837603 and 0.9590968 (1 point, 0.5 for some work, 0.5 for the correct answer. Reasonable rounding suffice) Question. Chap 15, # 49 (3 points) A package of light bulbs promises an average life of more than 750 hours per bulb. A consumer group did not believe the claim and tested a sample of 40 bulbs was 740 hours with s = 30 hours. The manufacturer responded that its claim was based on testing hundreds of bulbs. (a) (1 point) If the consumer group and manufacturer both make 95% confidence intervals for the population’s average lifetime, whose will probably be shorter? Can you tell for certain?
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