Chapter 12: Q. 12.94 (page 518)
For what purpose is a chi-square homogeneity test used?
To compare the distributions of a variable of two or more populations.
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12.50 U.S. Hospitals. The American Hospital Association publishes 12.30 U.S. information about U.S. hospitals and nursing homes in Hospital Statistics. The following contingency table provides a cross classification of U.S. hospitals and nursing homes by type of facility and number of beds.
In the following questions, the term hospital refers to either a hospital or nursing home.
| 24 or fewer | 25-74 | 75 or more | Total | |
| General | 260 | 1586 | 3557 | 5403 |
| Psychiatric | 24 | 242 | 471 | 737 |
| Chronic | 1 | 3 | 22 | 36 |
| Tuberculosis | 0 | 2 | 2 | 4 |
| Other | 25 | 177 | 208 | 410 |
| Total | 310 | 2010 | 4260 | 6580 |
a. How many hospitals have at least 75 beds?
b. How many hospitals are psychiatric facilities?
c. How many hospitals are psychiatric facilities with at least 75 beds?
d. How many hospitals either are psychiatric facilities or have at least 75 beds?
e. How many general facilities have between 25 and 74 beds?
f. How many hospitals with between 25 and 74 beds are chronic facilities?
g. How many hospitals have more than 24 beds?
Bottled Water. A project exploring the bottled-water phenomenon and preference of water types was conducted by researchers M. Lunsford and A. Fink in the article "Water Taste Test Data" (Journal of Statistics Education, Vol. 18, No. 1). One hundred nine subjects participated in double-blind taste tests of three different bottled water brands (Fiji, Aquafina, and Sam's Choice) and tap water. Twelve people preferred the tap water, 27 Aquafino 44 Fiji, and 26 Sam's Choice. At the 5% significance level, do the data provide sufficient evidence to conclude that the four different water types are not equally likely in preference?
Loaded Die? A gambler thinks a die may be loaded, that is, that the six numbers are not equally likely. To test his suspicion, he rolled the die 150 times and obtained the data shown in the following table.
Number | 1 | 2 | 3 | 4 | 5 | 6 |
Frequency | 23 | 26 | 23 | 21 | 31 | 26 |
In each of Exercises 12.11-12.16, we have given the relative frequencies for the null hypothesis of a chi-square goodness-of-fir text and the sample size. In each case, decide whether Assumptions 1 and 2 for using that text are satisfied.
Sample size : n= 100.
Relative frequencies: 0.44 , 0.25 , 0.30 , 0.01.
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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