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 0.05 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 Determine null hypothesis, Chi square test statistic, p value, critical value, conclusion, reject or fail to reject null hypothesis.

Male 308 156 58

Female 326 158 54

Answer 1

SOLUTION:

From given data,

	Human activity	Natural patterns	Don't know
Male	308	156	58
Female	326	158	54

Determine null hypothesis

The null hypothesis and the alternative hypothesis .

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

:the sex of the respondent is dependent of the choice for the cause of global warming.

Chi square test statistic

Add up rows and columns:

O	Human activity	Natural patterns	Don't know	Total
Male	308	156	58	522
Female	326	158	54	538
Total	634	314	112	1060

Calculate "Expected Value" for each entry:

Multiply each row total by each column total and divide by the overall total:

E = (Row total)(Column total) / Grand Total

E	Human activity	Natural patterns	Don't know
Male	(634*522)/1060= 312.21509	(314*522)/1060 =154.63019	(112*522)/1060 =55.15472
Female	(634*538)/1060 = 321.78491	(314*538)/1060 = 159.36981	(112*538)/1060 = 56.84528

Subtract expected from actual, square it, then divide by expected:

=

	Human activity	Natural patterns	Don't know
Male	(308-312.21509)^2/312.21509=0.056906	(156-154.63019)^2/154.63019=0.012135	(58-55.15472)^2/55.15472=0.146780
Female	(326-321.78491)^2/321.78491 = 0.055214	(158-159.36981)^2/159.36981=0.011773	(54-56.84528)^2/56.84528=0.142415

Now add up those values:

=   = 0.056906+0.012135+0.146780+0.055214+0.011773 +0.142415

= 0.42522

Chi-Square = = 0.42522

P- value

Calculate Degrees of Freedom

= (rows − 1) (columns − 1)

DF = (2 − 1)(3 − 1) = 1×2 = 2

P- value at   = 0.42522 with   DF = 2

P- value =0.80847

Critical value :

Critical value at   = 0.05 with   DF = 2

= 5.991

conclusion, reject or fail to reject null hypothesis.

the test statistic does not fall in the critical region,there is not sufficient evidence to reject the null hypothesis that row and column variables are independent.

There is not sufficient evidence to warrant rejection of the claim that the sex of the respondent is independent of the chore for the cause of global warming From the above results we conclude that, men and women appear to agree .

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