Question

In this article, Attitudes About Marijuana and Political Views (Psychological Reports, 1973), researchers reported on the use of cannabis by liberals and conservatives during the 1970s.

To test the claim (at 1% significance) that the proportion of voters who smoked cannabis frequently was lower among conservatives, the hypotheses were:
H0:p1−p2=0(p1=p2)
Ha:p1−p2<0(p1 In the hypothesis test about cannabis use by conservatives and liberals, the test statistic was z = -4.27, with a corresponding p-value of about 0.00001.
Which conclusion is most appropriate in the context of this situation?

Answer 1

Options :

Which conclusion is most appropriate in the context of this situation?

The data do not support the claim that a lower proportion of conservatives smoke cannabis when compared to liberals.

The data support the claim that the proportion of conservatives who smoke cannabis is no different that the proportion for liberals.

The data support the claim that a lower proportion of conservatives smoke cannabis when compared to liberals.

Answer:

The data support the claim that a lower proportion of conservatives smoke cannabis when compared to liberals.

Explanation:

Given the hypothesis :

H0:p1−p2=0(p1=p2)

Ha:p1−p2<0

The test statistic = - 4.27

Pvalue = 0.00001

For making statistical decisions ;

Pvalue and α are very useful,

Decison boundary :

When Pvalue ≤ α ; We reject the Null (H0) otherwise, we fail to reject the Null.

However, based on the outcome of the statistical analysis,

The Pvalue < α ; Hence, we reject the Null and conclude that there is significant evidence support the claim that a lower proportion of conservatives smoke cannabis when compared to liberals.