Mathematical Statistics with Applications
Mathematical Statistics with Applications
7th Edition
ISBN: 9781111798789
Author: Dennis O. Wackerly
Publisher: Cengage Learning
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Chapter 14.4, Problem 13E

On the 40th anniversary of President John F. Kennedy’s assassination, a FOX news poll showed that most Americans disagree with the government’s conclusions about the killing. The Warren Commission found that Lee Harvey Oswald acted alone when he shot Kennedy, but many Americans are not so sure about this conclusion. Do you think that we know all of the relevant facts associated with Kennedy’s assassination, or do you think that some information has been withheld? The following table contains the results of a nationwide poll of 900 registered voters.

Chapter 14.4, Problem 13E, On the 40th anniversary of President John F. Kennedys assassination, a FOX news poll showed that

  1. a Do the data provide sufficient evidence to indicate a dependence between party affiliation and opinion about a possible cover-up? Test using α = .05.
  2. b Give bounds for the associated p-value and interpret the result.
  3. c Applet Exercise Use the χ2 applet to obtain the approximate p-value.
  4. d Why is the value you obtained in part (c) “approximate”?
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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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