Question

In 1941​, 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, 385 indicated that they were total abstainers. In a recent​ survey, the same question was asked of 1100 adults and 363 indicated that they were total abstainers.

Determine the sample proportion for each sample?

Has the proportion of adults who totally abstain from alcohol​ changed? Use the

alphaαequals=0.050.05

level of significance.

First verify the model requirements. Select all that apply.

A. n 1 ModifyingAbove p with caret 1 left parenthesis 1 minus ModifyingAbove p with caret 1 right parenthesis greater than or equals 10n1p11−p1≥10 and n 2 ModifyingAbove p with caret 2 left parenthesis 1 minus ModifyingAbove p with caret 2 right parenthesis greater than or equals 10n2p21−p2≥10

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

C. The samples are dependent.

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

E. The samples are independent.

F. The data come from a population that is normally distributed.

Identify the null and alternative hypotheses for this test. Let p 1p1 represent the population proportion of 1941 adults who were total abstainers and p 2p2 represents the population proportion of recent adults who were total abstainers. Determine the null and alternative hypotheses.

Find the test statistic for this hypothesis test.

Determine the​ P-value for this hypothesis test.

If the population proportions are _, one would expect a sample difference proportion_ the one observed in about _

out of 100 repetitions of this experiment.

State the conclusion for this hypothesis test.

Answer 1

Explanation

Given data

The Following conditions are satisfied

A) We observe that at least 10 successes and 10 failures in each sample

and

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

E) The two samples should be independent random samples

F) The data come from the Normally distributed

Given First sample size

  

Given second sample size

  

The First sample proportion

The second sample proportion

Null hypothesis :  

Alternative hypothesis

Test Statistic

where

On Calculation, we get

Test statistic

Level of significance

The calculated Z = 1.0 < 1.96 at 5% level of significance

Null Hypothesis is Accepted

P-value:-

The Z-value = 1.0

P(Z> 1.0) = 1-P(Z<1)

= 1- (0.5+A(1))

= 1- (0.5 + 0.3413) [ from normal table]

= 0.5 - 0.3413

   P(Z>0.3134) = 0.1587

The P-value = 0.1587

Condition(i):-

P-value < then reject H0

Condition(ii):-

P-value > then Accept H0

Conclusion:-

P-value > then Accept H0

0.1587 > 0.05 then Accept H0

Accept null Hypothesis

There is significant difference between two sample proportions