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Chapter 11: Problem 6

Describe the four characteristics of a multinomial experiment.

Short Answer

Expert verified
A multinomial experiment has four key characteristics: 1. It consists of n repeated trials; 2. Each trial can result in one out of k possible outcomes; 3. The probabilities of the outcomes remain constant from trial to trial; 4. The variable of interest is the number of times each possible outcome occurs in n trials.

Step by step solution

01

Identify the first characteristic of a multinomial experiment

The first characteristic of a multinomial experiment is that it consists of n repeated trials. This means that the experiment is conducted multiple times under the same or similar conditions, and each trial is independent of each other.
02

Identify the second characteristic of a multinomial experiment

The second characteristic is that each trial can result in one of the k possible outcomes. In other words, there are k different outcomes possible for a single trial, where k is a number greater than or equal to 2. The outcomes are mutually exclusive, meaning each trial can end with just one outcome.
03

Identify the third characteristic of a multinomial experiment

The third characteristic is that the probabilities of the outcomes remain constant from trial to trial. The outcome of any particular trial does not affect the probabilities of the outcomes of the other trials.
04

Identify the fourth characteristic of a multinomial experiment

The fourth characteristic deals with the variable of interest. It counts the number of times each possible outcome occurs in n trials, forming a probability distribution.

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Most popular questions from this chapter

All shoplifting cases in the town of Seven Falls are randomly assigned to either Judge Stark or Judge Rivera. A citizens group wants to know whether either of the two judges is more likely to sentence the offenders to jail time. A sample of 180 recent shoplifting cases produced the following two-way table. $$ \begin{array}{llc} \hline & \text { Jail } & \text { Other Sentence } \\ \hline \text { Judge Stark } & 27 & 65 \\ \text { Judge Rivera } & 31 & 57 \\ \hline \end{array} $$ Test at a \(5 \%\) significance level whether the type of sentence for shoplifting depends on which judge tries the case.

In a Harris Poll conducted October \(15-20,2014\), American adults were asked "to think ahead 2 to 5 years and assess if they feel solar energy will contribute to meeting our energy needs." Of the respondents, \(31 \%\) said solar energy will make a major contribution to meeting our energy needs within the next 2 to 5 years, \(53 \%\) felt it will make a minor contribution, and \(16 \%\) expected that it will make hardly any contribution at all (www.harrisinteractive.com). Assume that these results are true for the 2014 population of adults. Recently a random sample of 2000 American adults was selected and these adults were asked the same question. The results of the poll are presented in the following table. $$ \begin{array}{l|ccc} \hline \text { Response } & \begin{array}{c} \text { Major } \\ \text { Contribution } \end{array} & \begin{array}{c} \text { Minor } \\ \text { Contribution } \end{array} & \begin{array}{c} \text { Hardly Any } \\ \text { Contribution } \end{array} \\ \hline \text { Frequency } & 820 & 920 & 260 \\ \hline \end{array} $$ Test at a \(2.5 \%\) significance level whether the current distribution of opinions to the said question is significantly different from that for the 2014 opinions.

A drug company is interested in investigating whether the color of their packaging has any impact on sales. To test this, they used five different colors (blue, green, orange, red, and yellow) for their packages of an over- the-counter pain reliever, instead of the traditional white package. The following table shows the number of packages of each color sold during the first month. $$ \begin{array}{l|ccccc} \hline \text { Package color } & \text { Blue } & \text { Green } & \text { Orange } & \text { Red } & \text { Yellow } \\ \hline \begin{array}{l} \text { Number of } \\ \text { packages sold } \end{array} & 310 & 292 & 280 & 216 & 296 \\ \hline \end{array} $$ Using a \(1 \%\) significance level, test the null hypothesis that the number of packages sold of each of these five colors is the same.

To make a goodness-of-fit test, what should be the minimum expected frequency for each category? What are the alternatives if this condition is not satisfied?

What is a goodness-of-fit test and when is it applied? Explain.
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