To determine the correct answer, let's first recall that the standard deviation of the sampling distribution of the difference between two sample proportions, [tex]\(\hat{p}_A - \hat{p}_T\)[/tex], can be calculated using the following formula:
[tex]\[ \text{SD}(\hat{p}_A - \hat{p}_T) = \sqrt{ \frac{p_A (1 - p_A)}{n_A} + \frac{p_T (1 - p_T)}{n_T} } \][/tex]
Where:
- [tex]\( p_A \)[/tex] is the population proportion of adults who read nonfiction books, which is 0.56.
- [tex]\( p_T \)[/tex] is the population proportion of teenagers who read nonfiction books, which is 0.39.
- [tex]\( n_A \)[/tex] is the sample size of adults, which is 28.
- [tex]\( n_T \)[/tex] is the sample size of teenagers, which is 41.
Given these values, the standard deviation can be interpreted as follows:
"The difference (adult - teenager) in the sample proportions of those who read nonfiction books as a hobby typically varies about 0.121 from the true difference in proportions."
Thus, the correct answer is:
The difference (adult - teenager) in the sample proportions of those who read nonfiction books as a hobby typically varies about 0.121 from the true difference in proportions.
