Question

In 1947​, 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, 363 indicated 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.

​(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 0.330 and 0.280​, respectively. ​

(Round to three decimal places as​ needed.)

​(b) Has the proportion of adults who totally abstain from alcohol​ changed? Use the α=0.05 level of significance.

First verify the model requirements. Select all that apply.

A.

The data come from a population that is normally distributed.

B.

n1p̂ 1(1−p̂ 1)≥10 and n2p2(1−p2)≥10

C.

The sample size is less than​ 5% of the population size for each sample.

D.

The samples are dependent.

E.

The samples are independent.

F.

The sample size is more than​ 5% of the population size for each sample.

Answer 1

A) The proportions calculate are correct.

B) To conduct a hypothesis test we assume a the following things

A.

The data come from a population that is normally distributed.

B.

n1p̂ 1(1−p̂ 1)≥10 and n2p2(1−p2)≥10

E.

The samples are independent.

F.

The sample size is more than​ 5% of the population size for each sample.

Conducting the hypothesis test. It is a two-tailed binomial proportion testing.

In words: Null Hypo: Proportion of people abstaining alcohol did not change from 1947

VS

Alternative Hypo: Proportion of people abstaining alcohol did change from 1947

and 'p' is the population paramter

Test Statistic:

Where and 'n = 1100' is the sample size

Decision Criteria:Reject null hypothesis if T.S > Critical value

Test Stat = = 3.5267

Critical Value = () ( the values can be found using normal dist tables or looked up online or using excel function 'normsinv')

T.S > Critical value

Decision: We reject null hypothesis at 5% level of significance and conclude that the proportion of people abstaining from drinking alcohol has change since 1947.