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Chapter 12: Q. 1 (page 520)

How do you distinguish among the infinitely many different chi-square distributions and their corresponding $x^{2}$ -curves?

Short Answer

Expert verified

The infinitely many different chi-square distributions and their corresponding $x^{2}$ -curves can be distinguished by their degrees of freedom.

Step by step solution

01

Step 1. Given information.

Consider the given question,

The corresponding $x^{2}$ curves.

02

Step 2. Differentiate by degrees of freedom.

We can differentiate the infinitely many different chi-square distributions and their corresponding $x^{2}$ curves by their degrees of freedom,

$d f = 5, 10, 19$

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Most popular questions from this chapter

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?

Presidential Election. According to Dave Leip's Atlas of U.S. Presidential Elections, in the 2012 presidential election, $51.01 %$ of those voting voted for the Democratic candidate (Barack H. Obama), whereas $57.50 %$ of those voting who lived in Illinois did so. For that presidential election, does an association exist between the variables "party of presidential candidate voted for" and "state of residence" for those who voted? Explain your answer.

In each of Exercises $12.24 - 12.33$ , apply the chi-square goodness-of-fit test, using either the critical-value approach or the $P -$ value approach, to perform the required hypothesis test.
Observing that the proportion of blue M&Ms in his bowl of candy appeared to be less than that of the other colors, R. Fricker, Jr., decided to compare the color distribution in randomly chosen bags of M&Ms to the theoretical distribution reported by M&M/MARS consumer affairs. Fricker published his findings in "The Mysterious Case of the Blue M&Ms" (Chance, Vol. 9(4), pp. 19-22). The following table gives the theoretical distribution.
For his study, Fricker bought three bags of M&Ms from local stores and counted the number of each color. The average number of each color in the three bags was distributed as follows.

Do the data provide sufficient evidence to conclude that the color distribution of M&Ms differs from that reported by M&M/MARS consumer affairs? Use $α = 0.05$ .

Education of Prisoners. Refer to Exercise 12.49.

a. Find the conditional distribution of educational attainment with in each type of prison facility.

b. Does an association exist between educational attainment and of prison facility for prisoners? Explain your answer.

c. Determine the marginal distribution of educational attainment for prisoners.

d. Construct a segmented bar graph for the conditional distributions of educational attainment and marginal distribution of educational attainment that you obtained in parts (a) and (c), respectively. 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 educational attainment categories are identical."

f. Determine the marginal distribution of facility type and the conditional distributions of facility type within educational attainment

categories.

g. Find the percentage of prisoners who are in federal facilities.

h. Find the percentage of prisoners with at most an 8th-gradetion who are in federal facilities.

i. Find the percentage of prisoners in federal facilities who have at most an 8th-grade education.

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

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