Question

Staying Single. From the U.S. Census Bureau document America's Families and Living Arrangements and an article in Time magazine, we found that, in $1963,83.0\%$of American women between the ages of $25and54$were married, compared to $64.6\%in2010$

a. For 2010 , identify the population.

b. For 2010 , identify the specified attribute.

c. Under what circumstances is the proportion $0.646$a population proportion?

d. Under what circumstances is the proportion$0.646$ a sample proportion?

Short answer

(a) For 2010 , the population would be American women between the ages of $25and54$

(b) For 2010 , specific attribute would be marital status of American women between the ages of $25and54$.

(c) All American women aged $25and54$would have made up the total population, with$64.6\%$of them married. And the population percentage is $64.6\%$

(d) The proportion $0.646$indicates a sample proportion of married American women between the ages of $25and54$.

Step-by-step solution

Part (a) Step 1: Given Information  

Given in the question that, in $1963,83.0\%$of American women between the ages of $25and54$were married, compared to $64.6\%in2010$. we have to find the population under consideration for the given scenario.

Part (a) Step 2: Explanation

In 2010, $64.6$percent of American women aged $25and54$were married, compared to 1963,$83.0$percent in 2010.

For the year 2010, the population would be American women aged $25and54$.

Part (b) Step 1: Given Information  

Given in the question that, in $1963,83.0\%$of American women between the ages of $25and54$were married, compared to $64.6\%in2010$. we have to find the specific attribute under consideration for the given scenario.

Part (b) Step 2: Explanation

In 2010, $64.6$percent of American women aged $25and54$were married, compared to$1963,83.0$percent in 2010.

The married status of American women between the ages of$25and54$would be a specific attribute for 2010.

Part (c) Step 1: Given Information  

Given in the question that, in $1963,83.0\%$,of American women between the ages of $25and54$were married, compared to $64.6\%in2010$we have to identify under what circumstances is the proportion $0.646$a population proportion.

Part (c) Step 2: Explanation

In 2010, $64.6\%$t of American women aged $25and54$were married, compared to 1963,$83.0\%in2010$

If the survey had been conducted solely in 2010, the population proportion would have been $0.646$. then all American women aged $25and54$would have made up the total population, with$64.6\%$of them married. And the population percentage is $64.6\%$.

Part (d) Step 1: Given Information  

Given in the question that, in $1983,83.0\%$of American women between the ages of $25and54$were married, compared to $64.6\%in2010$. we have to identify Under what circumstances is the proportion$0.646$ a sample proportion?

Part (d) Step 2: Explanation

In 2010, $64.6\%$of American women aged $25and54$were married, compared to 1963,$83.3\%in2010$.

The sample proportion in the current scenario is $0.646$. Because two sample surveys were conducted, one in 1963 and the other in 2010, so the proportion $0.646$indicates a sample proportion of married American women between the ages of $25and54$