Question

in october 1947, the gallup 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, 407 indicated that they were total abstainers. in a portion of the results of a recent survey, the same question was asked of 800 adults and 240 indicated that they were total abstainers. complete parts (a) and (b)
(a) determine the sample proportion for each sample.
the proportions of the adults who took the 1947 survey and the recent survey who were total abstainers are □ and □, respectively.
(round to three decimal places as needed.)

Explanation:

Step1: Calculate the sample proportion for 1947 survey

The formula for sample proportion $\hat{p}=\frac{x}{n}$, where $x$ is the number of successes (in this case, number of total abstainers) and $n$ is the sample size.
For 1947 survey, $x = 407$ and $n=1100$. So, $\hat{p}_{1947}=\frac{407}{1100}$
$$\hat{p}_{1947}=\frac{407}{1100}= 0.37$$

Step2: Calculate the sample proportion for recent survey

For recent survey, $x = 240$ and $n = 800$. So, $\hat{p}_{recent}=\frac{240}{800}$
$$\hat{p}_{recent}=\frac{240}{800}=0.3$$

Answer:

The proportions are \(0.370\) and \(0.300\)