K In 1948, an organization surveyed 1100 adults and asked, "Are you a total abstainer from, or do you on occasion consume, alcoholic beverages?" Of the 1100 adults surveyed, 374 indicated that they were total abstainers In a recent survey, the same question was asked of 1100 adults and 341 indicated that they were total abstainers. Complete parts (a) and (b) below.
E. The samples are dependent.
F. The data come from a population that is normally distributed.
Identify the null and alternative hypotheses for this test. Let $p_{1}$ represent the population proportion of 1948 adults who were total abstainers and $p_{2}$ represent the population proportion of recent adults who were total abstainers.
Determine the null and alternative hypotheses.
\[
\begin{array}{l}
H_{0}: p_{1}=p_{2} \\
H_{1}: p_{1} \neq p_{2}
\end{array}
\]

Find the test statistic for this hypothesis test.
(Round to two decimal places as needed.)

Step 1 ：Calculate the sample proportions for the two surveys. For the 1948 survey, the sample proportion (p1) is the number of total abstainers divided by the total number of adults surveyed. So, \(p1 = \frac{374}{1100} = 0.34\). For the recent survey, the sample proportion (p2) is also the number of total abstainers divided by the total number of adults surveyed. So, \(p2 = \frac{341}{1100} = 0.31\).

Step 2 ：Calculate the pooled proportion (p), which is the total number of abstainers from both surveys divided by the total number of adults surveyed in both surveys. So, \(p = \frac{(374 + 341)}{(1100 + 1100)} = 0.325\).

Step 3 ：Calculate the test statistic for this hypothesis test, which is a z-score. The formula for the z-score is \(z = \frac{(p1 - p2)}{\sqrt{p * (1 - p) * [(1/n1) + (1/n2)]}}\), where n1 and n2 are the sizes of the two samples, which are both 1100 in this case.

Step 4 ：Substitute the values into the z-score formula: \(z = \frac{(0.34 - 0.31)}{\sqrt{0.325 * (1 - 0.325) * [(1/1100) + (1/1100)]}}\).

Step 5 ：Simplify the expression to get the z-score: \(z = \frac{0.03}{\sqrt{0.325 * 0.675 * 0.00181818182}}\).

Step 6 ：Calculate the z-score: \(z = \frac{0.03}{0.0202020202}\).

Step 7 ：\(\boxed{z = 1.48}\)