STAT TECH IN BUSINESS & ECON AC
STAT TECH IN BUSINESS & ECON AC
18th Edition
ISBN: 9781264731657
Author: Lind
Publisher: MCG
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Chapter 13, Problem 35E

(a)

To determine

To create: The scatterplot of the data, and comment on the relationship.

(b)

To determine

To calculate: The correlation coefficient between the variables.

(c)

To determine

To transform: The variable x to x2 .

(d)

To determine

To create: The scatterplot of the transformed data, and comment on the relationship.

(e)

To determine

To calculate: The correlation coefficient between the transformed x and y .

(f)

To determine

To compare: The relationship between x and y, and x2 and y .

(g)

To determine

To interpret: The obtained results.

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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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STAT TECH IN BUSINESS & ECON AC

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