A public opinion poll surveyed a simple random sample of...

A public opinion poll surveyed a simple random sample of 1000 voters. Respondents were classified by gender (Male or Female) and by voting preference. The results are shown in the contingency table below: Republic Democrat Independent Total Male 200 150 50 400 Female 250 300 50 600 Total 450 450 100 1000 Test whether gender and voting preference are independent of each other. Use a significance level of 0.05. Please provide the steps, formulas, and explanations.

Transcript

00:01 So we would be assuming that gender and voting preference are independent, and alternately that the gender and voting preference are dependent.

00:19 I'm not going to write that all out.

00:21 And so that there is some type of a relationship between them.

00:25 Now, you had that contingency table, and so you had the republican, the democrat, the independent and then you had the total and you had male and you had female and then you had a total down here so they gave you all those totals that was nice and you had these values you had more females than you had males and these are both 50 and so this came to a total of 400 this came a total of 600 and these two added up to a thousand and these total to 450 these totaled to 450 and these total to 100.

01:04 Whoops, 100.

01:07 And so your first thing to do would be to find all of your expected values.

01:13 And so to find your expected values, remember we take our row totals, like for this first cell, and let's do it in red.

01:21 We would take our row total, whoops, and we get the row total, to find for this cell, which typically i just would write them underneath, and that 200 is there.

01:32 But i would take the row total 400 times the column total 450 divided by the table total which is a thousand and that would give me this first cell and that comes out to be 180 and likewise for this one and this will be the last one i'll do and i'll just write them down i would take my row total which is 400 times my column total which is 450 and then divided by the table total which is a thousand and we're going to get the same value here because those calculations are the same.

02:07 And this one comes out to be 40, this one comes out to be 60, this expected value comes out to be 270, and this becomes 270.

02:18 Now our kai squared statistic, which is the way we would analyze this, and again, i'm not going to write this all out, but i'll start it for you.

02:25 And the kai squared, and we would have for our degrees of freedom, by the way, we have two rows, so we take that less one.

02:33 And we have three columns and we take less one.

02:36 So our degrees of freedom is two...

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