Chapter 12: Q. 12.1 (page 484)
What is meant by saying that a variable has a chi-square distribution?
If the distribution contains the shape of a special type of right skewed curve which is called the chi-square curve, then the variable is said to have a chi-square distribution. It is denoted by .
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Job Satisfaction. A CNN/USA TODAY poll conducted by Gallul asked a sample of employed Americans the following question: "Which do you enjoy more, the hours when you are on your job, or the hours when you are not on your job?" The responses to this question were cross-tabulated against several characteristics, among which were gender, age, type of community, educational attainment, income, and type of employer. The data are provided on the WeissStats site. In each of Exercises 12.87-12.92, use the technology of your choice to decide, at the significance level, whether an association exists between the specified pair of variables.
type of community and response
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⋅n.
12.71 two and three
Consider a variable of several populations. Define the terms homogeneous and nonhomogeneous in this context.
Table 12.4 on page 486 showed the calculated sums of the observed frequencies, the expected frequencies, and their differences. Strictly speaking, those sums are not needed. However, they serve as a check for computational errors.
a) In general, what common value should the sum of the observer frequencies and the sum of the expected frequencies equal? Ex plain your answer.
b) Fill in the blank. The sum of the differences between each observed and expected frequency should equal
c) Suppose that you are conducting a chi-square goodness-of-fit test. If the sum of the expected frequencies does not equal the sample size, what do you conclude?
d) Suppose that you are conducting a chi-square goodness-of-fit test. If the sum of the expected frequencies equals the sample size, can you conclude that you made no error in calculating the expected frequencies? Explain your answer.
In given exercise use either the critical-value approach or the P-value approach to perform a chi square independence lest. provided the conditions for using the test are met.
Siskel In the classic TV show Sneak Previews, originally hosted by the late Gene Siskel and Roger Ebert, the two Chicago movie critics reviewed the weeks new movie releases and
then rated them thumbs up (positive), mixed, thumbs down (negative). These two critics often saw the merits of a movie differently. In general, however, were ratings given by Siskel and Ebert
associated? The answer to this question was the focus of the paper "Evaluating Agreement and Disagreement Among Movie Reviewers" by A. Agresti and L. Winner that appeared in Chance
(Vol- 10(2), pp-10-14). The following contingency table summarizes ratings by Siskel and Ebert for 160 movies.
At the 1% significance level, do the data provide sufficient evidence to conclude that an association exists between ratings of Siskel and Ebert?
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