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 :\(\boxed{z = 1.48}\)