Question

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 group20−24 years.
a. If there is no association exists between age group and gender, what percentage of the resident population would be in the age group20−24 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 group20−24 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 group20−24 years?
d. In fact, there are some 10.2 million female residents in the age group20−24 years. Given this number and your answer to part (c), what do you conclude?

Short answer

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

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

(c)The number of female residents would there be in the age group20−24 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

Part (a) Step 1. Given Information.

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

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 group20−24 years

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 group20−24 years

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 20−24 years if there is no association exists between age group and gender is given by,

$$\begin{gathered} =7.3\%of158 \\ =11.534million. \end{gathered}$$

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

The number of female residents would there be in the age group 20−24 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.