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A salesperson makes four calls per day. A sample of 100 days gives the following fre-quencies of sales volumes.$$ \begin{array}{l}{\text { Records show sales are made to } 30 \% \text { of all sales calls. Assuming independent sales calls, }} \\ {\text { the number of sales per day should follow a binomial distribution. The binomial probabil- }} \\ {\text { ity function presented in Chapter } 5 \text { is }}\end{array} $$$$ f(x)=\frac{n !}{x !(n-x) !} p^{x}(1-p)^{n-x} $$$$ \begin{array}{l}{\text { For this exercise, assume that the population has a binomial distribution with } n=4 \text { , }} \\ {p=.30, \text { and } x=0.1,2,3, \text { and } 4 .}\end{array} $$a. Compute the expected frequencies for $x=0,1,2,3,$ and 4 by using the binomial prob-ability function. Combine categories if necessary to satisfy the requirement that theexpected frequency is five or more for all categories.b. Use the goodness of fit test to determine whether the assumption of a binomial distri-bution should be rejected. Use $\alpha=.05$ . Because no parameters of the binomial dis-tribution were estimated from the sample data, the degrees of freedom are $k-1$ when $k$ is the number of categories.

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a. $24.01,41.16,26.46,8.37$b. There is not sufficient evidence to reject the claim of the binomialdistribution.

Intro Stats / AP Statistics

Chapter 11

Comparisons Involving Proportions and a Test of Independence

Descriptive Statistics

Confidence Intervals

The Chi-Square Distribution

Temple University

University of St. Thomas

Boston College

Lectures

0:00

01:49

Consider $n$ independent t…

02:11

In this exercise, we discu…

03:07

Probability In Exercises $…

05:20

Susan is a sales represent…

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