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Chapter 12: Q. 12.61 (page 502)

The U.S. Census Bureau publishes census data on the resident population of the United States in Current Population Reports. According to that document, 7.3% of male residents are in the age group20鈭�24 years.
a. If there is no association exists between age group and gender, what percentage of the resident population would be in the age group20鈭�24 years? Explain your answer.
b. If there is no association exists between age group and gender, what percentage of female residents would be in the age group20鈭�24 years? Explain your answer.
c. There are about 158million female residents of the United States. If no association exists between age group and gender, how many female residents would there be in the age group20鈭�24 years?
d. In fact, there are some 10.2 million female residents in the age group20鈭�24 years. Given this number and your answer to part (c), what do you conclude?

Short Answer

Expert verified

(a) If no association exists between age group and gender, 7.3%of the resident population would be in the age group 20鈭�24 years

(b) If there is no association exists between age group and gender, 7.3% of female residents would be in the age group 20鈭�24 years

(c)The number of female residents would there be in the age group20鈭�24 years if there is no association exists between age group and gender is 11.534million.

(d) We can conclude that there is an association between age group and gender.

Step by step solution

01

Part (a) Step 1. Given Information.

According to that document, 7.3% of male residents are in the age group 20鈭�24 years.

02

Part (a) Step 2. Find the percentage of the resident population.

If there is no association exists between age group and gender, then the percentage of conditional distribution of age group within the gender and the percentage of marginal age group are similar.

If no association exists between age group and gender, 7.3%of the resident population would be in the age group20鈭�24 years

03

Part (b) Step 1. Find the percentage of female residents.

If there is no association exists between age group and gender, then the percentage of conditional distribution of age group within the gender and the conditional distribution for each gender are identical.

If there is no association exists between age group and gender,7.3% of female residents would be in the age group20鈭�24 years

04

Part (c) Step 1. Find the number of female residents.

There are about 158 femal residents in the United States.

The number of female residents would there be in the age group 20鈭�24 years if there is no association exists between age group and gender is given by,

=7.3%of158=11.534million.

05

Part (d) Step 1. Conclusion from Part (c).

The number of female residents would there be in the age group 20鈭�24 years if there is no association exists between age group and gender is 11.534 million which is not same as the given number of female residents would there be in a age group of 20-24years of age.

We can conclude that there is an association between age group and gender.

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Most popular questions from this chapter

A poll conducted by Gallup asked American adults about vegetarianism. This problem is based on that poll. Of independent random samples of 500men and 512women, 20of the men and 36of the women said they were vegetarians. At the 5%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.

Regarding the expected-frequency assumptions for a chi-square goodness-of-fit test, a chi-square independence test, or a chi-square homogeneity test,

a. state them.

b. how important are they?

Job Satisfaction. A CNN/USA TODAY poll conducted by Gallul asked a sample of employed Americans the following question: "Which do you enjoy more, the hours when you are on your job, or the hours when you are not on your job?" The responses to this question were cross-tabulated against several characteristics, among which were gender, age, type of community, educational attainment, income, and type of employer. The data are provided on the WeissStats site. In each of Exercises 12.87-12.92, use the technology of your choice to decide, at the 5% significance level, whether an association exists between the specified pair of variables.

Educational attainment and response

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 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鈰卬.

12.74 six and seven
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