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Chapter 12: Q. 12.13 (page 491)
In each case, decide whether Assumptions and for using chi-square goodness-of-fit test are satisfied.
Sample size:.
Relative frequencies:.
Both Assumptionandare satisfied.
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Consider two curves with degrees of freedom and respectively. which one more closely resembles a normal curve? Explain your answer.
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?
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:
Observed frequencies:
Significance level
School Enrollment. Refer to Exercise 12:48. For students below postsecondary, solve the following problems.
a. Determine the conditional distribution of level for each gender.
b. Determine the marginal distribution of level.
c. Are the variables "gender"" and "level" associated? Explain your answer
d. Find the percentage of students in nursery school.
e. Find the percentage of females in nursery school.
f. Without doing any further calculations, respond true or false to the following statement and explain your answer: "The conditional distributions of gender within levels are not identical " .
g. Determine and interpret the marginal distribution of gender and the conditional distributions of gender within levels.
In each of Exercises 12.24-12.33, apply the chi-square goodness-of-fit test, using either the critical-value approach or thevalue approach, to perform the required hypothesis test.
An American roulette wheel contains red numbers, black numbers, and green numbers. The following table shows the frequency with which the ball landed on each color in trials.
At the significance level, do the data suggest that the wheel is out of balance?
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