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Chapter 11: Problem 8

Describe the four characteristics of a multinomial experiment.

Short Answer

Expert verified
A multinomial experiment has the following four characteristics: 1) It consists of n repeated trials. 2) Each trial results in a selection among several possible outcomes. 3) The probabilities of the outcomes remain constant from trial to trial. 4) The trials are independent.

Step by step solution

01

Describe the concept of repeated trials

One of the characteristics of a multinomial experiment is that it consists of a specified number of trials, often denoted by \( n \). These are events or observations which are repeated under the same set of conditions.
02

Discuss the possible outcomes

The second characteristic is that on each trial, a selection is made among several possible outcomes. The outcomes can be distinct and not just two as in a binomial experiment. Each outcome has an associated probability.
03

Discuss constant probabilities

The third characteristic is that the probabilities of the outcomes remain constant from trial to trial. This means that the experiment's conditions are not changing in a way that would alter the likelihood of the different results.
04

Discuss independence of trials

The final characteristic of a multinomial experiment is that the trials are independent. The result of one trial does not affect the result of another.

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Most popular questions from this chapter

Henderson Corporation makes metal sheets, among other products. When the process that is used to make metal sheets works properly, \(92 \%\) of the metal sheets contain no defects, \(5 \%\) have one defect each, and \(3 \%\) have two or more defects each. The quality control inspectors at the company take samples of metal sheets quite often and check them for defects. If the distribution of defects for a sample is significantly different from the above-mentioned percentage distribution, the process is stopped and adjusted. A recent sample of 300 sheets produced the frequency distribution of defects listed in the following table. $$ \begin{array}{l|ccc} \hline \text { Number of defects } & \text { None } & \text { One } & \text { Two or More } \\ \hline \text { Number of metal sheets } & 262 & 24 & 14 \\ \hline \end{array} $$ Does the evidence from this sample suggest that the process needs an adjustment? Use \(\alpha=.01\).

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

A sample of 21 observations selected from a normally distributed population produced a sample variance of \(1.97 .\) a. Write the null and alternative hypotheses to test whether the population variance is greater than \(1.75\). b. Using \(\alpha=.025\), find the critical value of \(\chi^{2}\). Show the rejection and nonrejection regions on a chi-square distribution curve. c. Find the value of the test statistic \(\chi^{2}\). d. Using a \(2.5 \%\) significance level, will you reject the null hypothesis stated in part a?

Construct the \(95 \%\) confidence intervals for the population variance and standard deviation for the following data, assuming that the respective populations are (approximately) normally distributed. a. \(n=10, s^{2}=7.2 \quad\) b. \(n=18, s^{2}=14.8\)

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?
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