A poll was conducted to investigate opinions about global...

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 Male 326 173 36 Female 335 167 33 Identify the null and alternative hypotheses. Compute the test statistic. (Round to three decimal places as needed.) Find the critical value(s). (Round to three decimal places as needed. Use a comma to separate answers as needed.) What is the conclusion based on the hypothesis test?

Transcript

00:01 So for this problem, what we need to do first is find our row and column totals.

00:06 So we can see that the total across row one, which i'll call r1, is 326 plus 173 plus 36, 535 for r1.

00:17 One second here, let me just, r1.

00:21 Total across r2 is 335 plus 167 plus 33.

00:26 So the total across r2 is equal to that across r1.

00:30 So that's 535 as well.

00:34 Then we want to find the total across our different columns.

00:38 So we'll have total across c1 is 326 plus 335, 161.

00:45 Cross the second column, c2 is 173 plus 167.

00:52 So that's 140.

00:57 And total across column 3.

01:00 It's going to be equal to 36, 36 plus 33.

01:05 So that's 69.

01:08 Now, what we want to do next is compute the expected value for each one of the cells, so row i column j, by taking the product, the total across row i, with the total across column j, divided by the grand total, which i'll call big n.

01:28 And we can find the grand total, for instance, just by adding together r1 and r2.

01:33 So we can see that big n is equal to 170.

01:41 So based on this, we can see that e11 is going to be row 1, which is 535 times column 1, divided by 1070.

01:56 So expect of value 1 1 is 330 .5, e12.

02:04 So that's row 1, column 2, 170.

02:10 Actually, i'll arrange these in a vague.

02:13 Grid -like pattern there.

02:16 And then e13, row one column three, that is equal to 34 .5.

02:25 Then we need to go through and do the same process with row two column one first.

02:30 We'll have e21, it's equal to 330 .5.

02:35 Row two, column two, e2, it's equal to 170.

02:44 And row 3, or row 2 column 3, e23, is equal to 34 .5.

02:54 Now that we have these, what we want to do is calculate out.

03:01 I'll call little r for the residual ij, which we find by taking the difference between the observed value and the expected value in each one of the cells, squaring that, and then dividing by the expected value in each one of the cells, squaring that, and then dividing by the expected value in each one of the...

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