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Chapter 11: Q.55 (page 730)

The degrees of freedom for the chi-square test for this two-way table are (a) 4.

(b) 8.

(c) 10.

(d) 20.

(e) None of these.

Short Answer

Expert verified

The degree of freedom is 4. Therefore, the correct option is (a).

Step by step solution

01

Given Information

The table is

02

Explanation

The degree of freedom is computed as:

Degree of freedom =Number of categories -1

=5-1

=4

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Most popular questions from this chapter

Gastric freezing was once a recommended treatment for ulcers in the upper intestine. The use of gastric freezing stopped after experiments showed it had no effect. One randomized comparative experiment found that 28of the 82gastric-freezing patients improved, while 30of the 78patients in the placebo group improved. We can test the hypothesis of 鈥渘o difference鈥� in the effectiveness of the treatments in two ways: with a two-sample z test or with a chi-square test.

(a) Minitab output for a chi-square test is shown below. State appropriate hypotheses and interpret the P-value in context. What conclusion would you draw?

Chi-Square Test: Gastric freezing, Placebo Expected counts are printed below observed counts Chi-Square contributions are printed below expected counts

(b) Minitab output for a two-sample z test is shown below. Explain how these results are consistent with the test in part (a).

Perform a follow-up analysis of the test in Exercise 40 by finding the individual components of the chi-square statistic. Which cell(s) contributed most to the final result?

The General Social Survey asked a random sample of adults their opinion about whether astrology is very scientific, sort of scientific, or not at all scientific. Here is a two-way table of counts for people in the sample who had three levels of higher education:

(a) Make a bar graph that compares opinions about astrology for the three education categories. Describe what you see.

(b) Minitab output for a chi-square test using these data is shown below. Carry out the test. What conclusion do you draw?

A chi-square goodness-of-fit test is used to test whether a 0 to 9 spinner is "fair" (that is, the outcomes are all equally likely). The spinner is spun 100 times, and the results are recorded. The degrees of freedom for the test will be

(a) 8 .

(c) 10 .

(e) None of these.

(b) 9 .

(d) 99.

Perform a follow-up analysis of the test in Exercise 39 by finding the individual components of the chi-square statistic. Which cell(s) contributed most to the final result?
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