BASIC PRACTICE OF STATISTICS(REISSUE)>C
BASIC PRACTICE OF STATISTICS(REISSUE)>C
8th Edition
ISBN: 9781319341831
Author: Moore
Publisher: MAC HIGHER
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Chapter 25, Problem 25.47E

a.

To determine

To show: Whether chi-square test of independence or homogeneity can be used for the given data.

b.

To determine

To test:Whether there is any relationship between thechronic kidney diseaseand hearing loss.

To state: The hypotheses used for testing, test statistic, P-value and conclusion.

c.

To determine

To identify: The variable type for “Age”.

To explain: The reason for using age to establish the relationship between eGFRdisease and hearing loss.

d.

To determine

To explain: Whether age can be used to establish the relationship between the chronic kidney diseases and hear loss if a separate two way table is constructed for the age groups 50, 51.

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iid 1. The CLT provides an approximate sampling distribution for the arithmetic average Ỹ of a random sample Y₁, . . ., Yn f(y). The parameters of the approximate sampling distribution depend on the mean and variance of the underlying random variables (i.e., the population mean and variance). The approximation can be written to emphasize this, using the expec- tation and variance of one of the random variables in the sample instead of the parameters μ, 02: YNEY, · (1 (EY,, varyi n For the following population distributions f, write the approximate distribution of the sample mean. (a) Exponential with rate ẞ: f(y) = ß exp{−ßy} 1 (b) Chi-square with degrees of freedom: f(y) = ( 4 ) 2 y = exp { — ½/ } г( (c) Poisson with rate λ: P(Y = y) = exp(-\} > y! y²
2. Let Y₁,……., Y be a random sample with common mean μ and common variance σ². Use the CLT to write an expression approximating the CDF P(Ỹ ≤ x) in terms of µ, σ² and n, and the standard normal CDF Fz(·).
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