# 409Hw04ans - STAT 409 Homework #4 ( due Friday, September...

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STAT 409 Homework #4 Fall 2011 ( due Friday, September 23, by 4:00 p.m. ) 1. A random sample of 9 adult elephants had the sample mean weight of 12,240 pounds and the sample standard deviation of 450 pounds. A random sample of 16 adult hippos had the sample mean weight of 5,700 pounds and the sample standard deviation of 400 pounds. Assume that the two populations are approximately normally distributed, Construct a 95% confidence interval for the difference between their overall average weights of adult elephants and adult hippos. a) Assume that the overall standard deviations are equal. ( ) ( ) 2 16 9 400 1 16 450 1 9 2 2 2 pooled - + - + - = s 174,782.6 pooled s 418.07 ( ) m n s t 1 1 Y X pooled 2 + ± - α 9 + 16 – 2 = 23 degrees of freedom t 0.025 ( 23 ) = 2.069 ( ) 16 1 9 1 07 . 418 069 . 2 700 , 5 240 , 12 + ± - 6,540 ± 360.4 ( 6,179.6 , 6,900.4 ) b) Do NOT assume that the overall standard deviations are equal. Use Welch’s T. - + - + 1 1 1 1 2 2 2 2 2 2 1 2 1 1 2 2 2 2 1 2 1 n n n n n n s s s s = - + - + 16 400 1 16 1 9 450 1 9 1 16 400 9 450 2 2 2 2 2 2 2 =   15.1 = 15 degrees of freedom t 0.025 ( 15 ) = 2.131 ( ) 16 400 9 450 131 . 2 700 , 5 240 , 12 2 2 + ± - 6,540 ± 384.17 ( 6,155.83 , 6924.17 )

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2. The service time in queues should not have a large variance; otherwise, the queue tends to build up. A bank regularly checks service time by its tellers to determine its variance. A random sample of 22 service times (in minutes) gives s 2 = 8. Assume the service times are normally distributed.
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## This note was uploaded on 10/13/2011 for the course STAT 409 taught by Professor Stephanov during the Fall '11 term at University of Illinois at Urbana–Champaign.

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409Hw04ans - STAT 409 Homework #4 ( due Friday, September...

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