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Unformatted text preview: Economics 70 Answer Key to Book Problem 5 Exercise Title: Homework No. 5 Date: 5/6/2009 Name (Last, First): Answer Key PID: Section No. of Course: Sections 1 & 2 Sign the Honor Pledge: 6.1 Regardless of the shape of the population from which we are sampling, the sampling distribution of the sample mean will have a mean equal to the mean of the population from which we are sampling, and a standard deviation equal to . n a) ( 29 = = x E 10; 6 . 25 3 = = = n x b) ( 29 = = x E 5; 2 . 100 2 = = = n x c) ( 29 = = x E 120; 4082 . 6 1 = = = n x 6.2 a) If the sampled populations are normal, the distribution of x is also normal for all values of n. b) The Central Limit Theorem states that for sample sizes as small as n = 25, the sampling distribution of x will be approximately normal. Hence, we can be relatively certain that the sampling distribution of x for parts a and b will be approximately normal. However, the sample size in part c, n = 6, is too small to assume that the distribution of x is approximately normal. 6.3 a) The sketch of the normal distribution with mean equal to 5 and standard deviation equal to 0.2 is left to the student. The interval 5 .4 or 4.6 to 5.4 should be located on the x axis. b) The probability of interest is P ( 29 [ ] 15 . 15 . <- <- x . c) P ( 29 [ ] 15 . 15 . <- <- x = P ( 29 <- <- 2 ....
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- Spring '08