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Chapter 12: Q. 12.47 (page 500)

AIDS Cases. According to the Centers for Disease Control and Prevention publication HIV Surveillance Report, the number of AIDS cases in the United States in 2011, by region and race, is as shown in the following contingency table.

RegionWhiteBlackOtherTotal
Northeast1,1002,493
5,177
Northwest1,137
5043221
South2,7617,848
12,867
West
76417664,230
Total

605225,435

a. How many cells does this contingency table have?

b. Fill in the missing entries.

c. What was the total number of AIDS cases in the United States in 2011?

d. How many AIDS cases were whites?

e. How many AIDS cases were Southerners?

f. How many AIDS cases were black Westerners?

Short Answer

Expert verified

(a) 12 cells

(b)

RegionWhiteBlackOtherTotal
Northeast1,1002,4931,5245,177
Northwest1,1371,5805043221
South2,7617,8482,25812,867
West1,70076417664,230
Total6,69812,685605225,435

(c)The total number of aids cases in the United states in 2011 is 25,435.

(d) 6698

(e) 12,867

(f) 764

Step by step solution

01

Given 

The given table is

RegionWhiteBlackOtherTotal





Northeast1,1002,493
5,177
Northwest1,137
5043221
South2,7617,848
12,867
West
76417664,230
Total

605225,435
02

Part a. Step 2. Total number of cell

There are 12 cell in contingency table

03

Part b. Step 3. The missing value 

RegionWhiteBlackOtherTotal
Northeast1,1002,4931,5245,177
Northwest1,1371,5805043221
South2,7617,8482,25812,867
West1,70076417664,230
Total6,69812,685605225,435
04

Part c. Step 4. The total no of aids

The total number of aids cases in the United states in 2011 is 25,435.

05

Part d. Step 5. Finding the number of aids cases were white.

The total number of AIDS cases were whites is

1,100+1,137+2,761+1,700=6,698

06

Part e. Step 6. Finding the number of AIDS cases were Southerners 

The total number of AIDS cases were southerners

2,761+7,848+2,258=12,867

07

Part f. Step 7.  Finding the number of AIDS cases were Westerners

The number of AIDS cases were Westerners

764.

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Most popular questions from this chapter

We have presented a contingency table that gives a cross-classification of a random sample of values for two variables x and y, of a population.

Perform the following tasks

a. Find the expected frequencies Note: You will first need to compute the row totals, column totals, and grand total.

b. Determine the value of the chi-square statistic

c. Decide at the 5% significance level whether the data provide sufficient evidence to conclude that the two variables are associated.

To decide whether two variables of a population are associated, we usually need to resort to inferential methods such as the chi-square independence test. Why?

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: 0.2,0.1,0.1,0.3,0.3

Observed frequencies: 29,13,5,25,28

Significance level =0.10

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.

12.69 four and five

For what purpose is a chi-square homogeneity test used?
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