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Chapter 12: Q. 12.99 (page 518)
A chi-square homogeneity test is to be conducted to decide whether a difference exists among the distributions of a variable of six populations. The variable has five possible values. What are the degrees of freedom for the x2-statistic?
Degrees of freedom for the x2-statistic is given by
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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?
US. Hospitals. Refer to Exercise 12.50.
| 24 or fewer | 25-74 | 75 or more | Total | |
| General | 260 | 1586 | 3557 | 5403 |
| Psychiatric | 24 | 242 | 471 | 737 |
| Chronic | 1 | 3 | 22 | 26 |
| Tuberculosis | 0 | 2 | 2 | 4 |
| Other | 25 | 177 | 208 | 410 |
| Total | 310 | 2010 | 4260 | 6580 |
a. Determine the conditional distribution of number of beds within each facility type.
b. Does an association exist between facility type and number of beds for U.S. hospitals? Explain your answer.
c. Determine the marginal distribution of number of beds for U.S. hospitals.
d. Construct a segmented bar graph for the conditional distributions and marginal distribution of number of beds. Interpret the graph in light of your answer to part (b),
e. Without doing any further calculations, respond true or false to the following statement and explain your answer. "The conditional distributions of facility type within number-of-beds categories are identical.
f. Determine the marginal distribution of facility type and the conditional distributions of facility type within number-of-beds categories.
g. What percentage of hospitals are general facilities?
h. What percentage of hospitals that have at least 75 beds are general facilities?
i. What percentage of general facilities have at least 75 beds?
A poll conducted by Gallup asked American adults about vegetarianism. This problem is based on that poll. Of independent random samples of men and women, of the men and of the women said they were vegetarians. At the significance level do the data provide sufficient level do the data provide sufficient evidence to conclude that a difference exists in the proportions of male and female vegetarians?
Part (a): Use the two-portions z-test to perform the required hypothesis test.
Part (b): Use the chi-square homogeneity test to perform the required hypothesis test.
Part (c): Compare your results in parts (a) and (b).
Part (d): Explain what principle is being illustrated.
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, 0.4, 0.3, 0.1
Observed frequencies: 85, 215, 130, 70
Significance level = 0.05
In Exercises 12.101-12.106, tase either the critical-value approach or the P-value approach to perform a chi-square homogeneity test, provided the conditions for using the test are met.
12.101 Self-Concept and Sightedness. Self-concept can be defined as the general view of oneself in terms of personal value and capabilities. A study of whether visual impairment affects self-concept was reported in the article "An Exploration into Self Concept: A Comrarative Analysis between the Adolescents Who Are Sighted and
Elind in India" (British Journal of Visual Impairment, Vol. 30, No. 1, of sighted and blind Indian adolescents gave the following data on self-concept.
a. At the 5% significance level, do the data provide sufficient evidence to conclude that a difference exists in self-concept distributions between sighted and blind Indian adolescents?
b. Repeat part (a) at the1%significance level.
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