hw8.solu

hw8.solu - STA 13A HW8 Solutions 7.19 Regardless of the...

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7.19 Regardless of the shape of the population from which we are sampling, the sampling distribution of the sample mean will have a mean µ equal to the mean of the population from which we are sampling, and a standard deviation equal to n σ . a 10; 3 36 .5 n µσ = = b 5; 2 100 .2 n = = c 120; 1 8 .3536 n = = = 7.20 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 25 n = , 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 is part c , 8 n = , is too small to assume that the distribution of x is approximately normal. 7.23 For a population with 1 = , the standard error of the mean is 1 nn = The values of n for various values of n are tabulated below and plotted below. Notice that the standard error decreases as the sample size increases . n 1 2 4 9 16 25 100 () SE x n = 1.00 .707 .500 .333 .250 .200 .100 7.25 a If the sample population is normal, the sampling distribution of x will also be normal (regardless of the sample size) with mean 106 = and standard deviation (or standard error ) given as 12 25 2.4 n = b Calculate 110 106 1.67 2.4 x z n −− = = , so that ( ) ( ) 110 1.67 1 .9525 .0475 Px Pz >= > = = c ( ) ( ) 102 110 1.67 1.67 .9525 .0475 .9050 P z << = = = 7.26 a Since the sample size is large, the sampling distribution of x will be approximately normal with mean 64,571 = and standard deviation 4000 60 516.3978 n = = .
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This note was uploaded on 02/27/2012 for the course STA 13 taught by Professor Samaniego during the Spring '10 term at UC Davis.

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hw8.solu - STA 13A HW8 Solutions 7.19 Regardless of the...

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