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Chapter 12: Q. 3 (page 520)

Recall that the number of degrees of freedom for the t-distribution used in a one-mean t-test depends on the sample size. Is that true for the chi-square distribution used in a chi-square.

Part (a): Goodness-of-fit test?

Part (b): Independence test?

Part (c): Homogeneity test?

Explain your answers.

Short Answer

Expert verified

Part (a): No. The degrees of freedom for the chi-square goodness-of-fit test depends only upon the number of possible values for the variable under consideration.

Part (b): No. The degrees of freedom for the chi-square independence test depends only upon the number of possible values for the two variables under consideration.

Part (c): No. The degrees of freedom for the chi-square homogeneity test depends only upon the number of possible values for the variable under consideration.

Step by step solution

01

Part (a) Step 1. Given information.

It is given that the number of degrees of freedom for the t-distribution used in a one-mean t-test depends on the sample size.

02

Part (a) Step 2. Goodness-of-fit test is used.

The number of degrees of freedom for the t-distribution which is used in one-mean t-test depends on the sample size. While the chi-square distribution used in a chi-square goodness-of-fit test is not true as the degrees of freedom for the chi-square goodness-of-fit test under consideration depends on the number of possible values for the variable and not on the sample size.

03

Part (b) Step 1. Independence test is used.

The number of degrees of freedom for the t-distribution which is used in a one-mean t-test depends on the sample size. The chi-square distribution used in a chi-square independence test is not true as the degrees of freedom for the chi-square independence test under consideration depends on the number of possible values for the two variables and not on the sample size.

04

Part (c) Step 1. Homogeneity test is used.

The number of degrees of freedom for the t-distribution which is used in a one-mean t-test depends on the sample size. The chi-square distribution used in a chi-square homogeneity test is not true as the degrees of freedom for the chi-square homogeneity test under consideration depends on the number of possible values for the variable and not on the sample size.

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Most popular questions from this chapter

In each of Exercises 12.18-12.23, we have provided a distribution and the observed frequencies of the values of a variable from a simple random sample of a population. In each case, use the chi-square goodness-of-fit test to decide, at the specified significance level, whether the distribution of the variable differs from the given distribution.

Distribution:0.5,0.3,0.2

Observed frequencies:147,115,88

Significance level=0.01

In each of the given Exercises, we have given the number of possible values for two variables of a population. For each exercise, determine the maximum number of expected frequencies that can be less than 5 in order that Assumption 2 of Procedure 12.2 on page 506 to be satisfied. Note: The number of cells for a contingency table with m rows and n columns is m鈰卬.

12.71 two and three

In each of the given Exercises, we have presented a contingency table that gives a cross-classification of a random sample of values for two variables, x, and y, of a population. For each exercise, perform the following tasks.

a. Find the expected frequencies. Note: You will first need to compute the row totals, column totals, and grand total.

b. Determine the value of the chi-square statistic.

c. Decide at the 5% significance level whether the data provide sufficient evidence to conclude that the two variables are associated.

For a 蠂2curve with 22degrees of freedom, determine the 蠂2value that has area

a. 0.01to its right.

b. 0.005to its right.

In each of Exercises 12.18-12.23, we have provided a distribution and the observed frequencies of the values of a variable from a simple random sample of a population. In each case, use the chi-square goodness-of-fit test to decide, at the specified significance level, whether the distribution of the variable differs from the given distribution.

Distribution: 0.2,0.1,0.1,0.3,0.3

Observed frequencies: 29,13,5,25,28

Significance level =0.10
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