Question

In 1946​, 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, 374indicated that they were total abstainers. In a recent​ survey, the same question was asked of 1100 adults and 308 indicated that they were total abstainers. Complete parts​ (a) and​ (b) below.

A: Determine the sample proportion for each sample.

The proportions of the adults who took the 1946 survey and the recent survey who were total abstainers are ___ and ___ ​, respectively.

​(Round to three decimal places as​ needed.)

B:

Has the proportion of adults who totally abstain from alcohol​ changed? Use the a=0.10 level of significance.

Answer 1

Given:

Sample 1 : 1946 survey

Number of adults surveyed : sample size : n₁ = 1100

Number of adults who  totally abstain from alcohol​ : x₁ = 374

: Sample proportion of adults who totally abstain from alcohol = x₁ / n₁ = 374/1100=0.34

Sample 2 : recent survey

Number of adults surveyed : sample size : n₂ = 1100

Number of adults who  totally abstain from alcohol​ : x₂ = 308

Sample proportion of adults who totally abstain from alcohol = x₂ / n₂= 308/1100=0.28

A; The proportions of the adults who took the 1946 survey and the recent survey who were total abstainers are  0.34  and  0.28​, respectively.

B :

p₁ : Population proportion of adults who totally abstain from alcohol as per 1946 survey

p₂ : Population proportion of adults who totally abstain from alcohol as per recent survey

Null hypothesis :H_o : Proportion of adults who totally abstain from alcohol​ have not changed ; p₁ = p₂

Alternate hypothesis : H_a : Proportion of adults who totally abstain from alcohol​ changed p₁ p₂ : Two Tailed test

Test statistic z = 3.0425

For Two tailed test :

As p-value : 0.0024 < : 0.10 ; Reject null hypothesis.

There is sufficient evidence to conclude that the proportion of adults who totally abstain from alcohol​ changed