Question

An organization surveyed 1,100 adults and​ asked, "Are you a total abstainer​ from, or do you on occasion​ consume, alcoholic​ beverages?" Of the 1,100 adults​ surveyed, 363 indicated that they were total abstainers. Sixty years​ later, the same question was asked of 1,100 adults and 435 indicated that they were total abstainers. Has the proportion of adults who totally abstain from alcohol​ changed? Use the a equals 0.=0.10 level of significance.

Answer 1

We have to test the hypothesis for proportion difference.

sample proportion 1 =

Sample proportion 2 =

pooled proportion =

We have to test whether there is any change in the proportions or not.

For null hypothesis, we will assume that there is no change in the proportions and for alternate hypothesis, we will assume that there is a change in the proportions.

Null hypothesis

Alternate hypothesis

calculation for test statistic, we will be using z test statistic for testing the difference in proportions

Formula for test statistics is given as

z =

setting the given values, we get

z =

this gives

z=

Using the z calculated value and 0.10 level of significance, using z distribution table

we get

p value for two tailed hypothesis = 0.0006

So, p value is less than 0.10 level of significance, this means that the p value is significant and result is also significant.

We can reject the null hypothesis and we can conclude that there is a significant change in the proportion of adults who totally abstain from alcohol.