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Category > Statistics Posted 25 Apr 2017 My Price 10.00

Central Limit Theorem

Refer to Exercise 7.60. Suppose that n1 = n2 = n, and find the value of n that allows the difference between the sample means to be within .04 unit of μ1 − μ2 with probability .90.

Exercise 7.60

The result in Exercise 7.58 holds even if the sample sizes differ. That is, if X1, X2, . . . , Xn1 and Y1, Y2, . . . , Yn2 constitute independent random samples from populations with means μ1 and μ2 and variances   and , respectively, then X − Y will be approximately normally distributed, for large n1 and n2, with mean μ1 − μ2 and variance  The flow of water through soil depends on, among other things, the porosity (volume

proportion of voids) of the soil. To compare two types of sandy soil, n1 = 50 measurements are to be taken on the porosity of soil A and n2 = 100 measurements are to be taken on soil B.

Exercise 7.58

Suppose that X1, X2, . . . , Xn and Y1, Y2, . . . , Yn are independent random samples from populations with means μ1 and μ2 and variances  and  respectively. Show that the random variable

satisfies the conditions of Theorem 7.4 and thus that the distribution function of Un converges to a standard normal distribution function as n → ∞.

Theorem 7.4

 

 

 

 

 
 

Answers

Alpha Geek
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Status NEW Posted 25 Apr 2017 08:04 AM My Price 10.00

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