Elementary Statistics
Elementary Statistics
12th Edition
ISBN: 9780321837936
Author: Mario F. Triola
Publisher: PEARSON
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Chapter 12, Problem 1TP

Chocolate Chips Revisited The Chapter Problem for Chapter 3 includes counts of chocolate chips in cookies from five different brands. The counts were obtained by the author. Use the counts listed in Table 3-1 with technology to conduct a test of the null hypothesis that the brands of Chips Ahoy (regular), Chips Ahoy (chewy). Chips Ahoy (reduced fat), Keebler, and Hannaford have the same mean number of chocolate chips. Obtain a printout of the results from technology. (If using a TI-83/84 Plus calculator, write the exact results displayed on the screen.) Write a brief report that includes comments about a check of the requirements and a statement of the final conclusion. After completing the analysis of variance test, explore the data and comment on any notable differences among the numbers of chocolate chips in the five brands.

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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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Elementary Statistics

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Chi Square test; Author: Vectors Academy;https://www.youtube.com/watch?v=f53nXHoMXx4;License: Standard YouTube License, CC-BY