A poll was conducted to investigate opinions about global warming. The responden

Question

A poll was conducted to investigate opinions about global warming. The respondents who answered yes when asked if there is solid evidence that the earth is getting warmer were then asked to select a cause of global warming. The results are given in the accompanying data table. Use a 0.01 significance level to test the claim that the sex of the respondent is independent of the choice for the cause of global warming. Do men and women appear to agree, or is there a substantial difference?

Human Activity Natural Patterns Don't know

Male 323 158 39

Female 340 152 38

a.compute the test statistic?

b.find the critical value?

Explanation / Answer

The problem boils down to the following hypotheses:

Ho: Sex of the respondent is independent of the choice for the cause of global warming.

H1: Sex of the respondent is dependent on the choice for the cause of global warming.

Chosen level of significance: 0.01

Original Table ,also showing marginals and grand total

Table of expected values :

Test Statistic: X2 = (323-328.343)2 / 328.343 + (158-153.524)2 /153.524 + (39-38.133)2 / 38.133 + (340-334.657)2 /334.657 + (152-156.476)2 / 156.476 + ( 38-38.867)2 /38.867

= 0.46974 (approx) = (value of test statistic)

degree of freedom = (2-1)*(3-1)= 2

Therefore, X2 critical (critical value) = 9.210

So, we see that the value of the chi square test statistic is less than the critical value for alpha=0.01

( 0.46974 < 9.210)

So, we fail to reject the null hypothesis,

and hence conclude that: Sex of the respondent is independent of the choice for the cause of global warming.

Human Activity Natural Patterns Don't Know Marginal Total Male 323 158 39 520 Female 340 152 38 530 Marginal Total 663 310 77 1050(= Grand total)

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