A study examined parental influence on teenagers decisions...

A study examined parental influence on teenagers' decisions to smoke. A group of students who had never smoked were questioned about their parents' attitudes toward smoking. These students were questioned again two years later to see if they had started smoking. The researchers found that, among the 265 students who indicated that their parents disapproved of kids smoking, 74 had become established smokers. Among the 49 students who initially said their parents were lenient about smoking, 17 became smokers. Do these data provide strong evidence that parental attitude influences teenagers' decisions about smoking? Use a 5% significance level.

Transcript

00:01 So for this problem, the approach that we'll take here is first to fill out a table where we basically have our different categories here.

00:08 So we have, for disapprove and smokers, we're told that among the 265 students who indicated that their parents disapproved of kids smoking, 74 became established smokers.

00:21 So 265 minus 74 did not.

00:26 And then for the lenient group, we have 17 out of the 4.

00:31 29 became smokers.

00:33 So the non -smokers would be 49 minus 17 for a result of 32.

00:38 Now the approach that we'll take here is that of a kai squared test for independence.

00:46 So our kai squared statistic is going to be the sum of the difference between the observed frequency and the expected frequency squared divided by the expected frequency for each one of the categories.

00:57 To find the expected frequencies, what we'll have to do is, first, find our totals across each row and each column.

01:07 So, taking our column totals, 74 plus 17, gives us 91, then 191 plus 32, gives us 23.

01:19 Then we know that our row totals would be 265 and 74.

01:28 Then to find the expected values for each one of our categories there, we basically just take the product of our totals along each row and each column divided by the grand total.

01:43 So we'll also need to figure out what the grand total is.

01:47 So that would be 91 plus 223 for a result of 314.

01:55 Okay.

01:56 So our grand total is 314...

Question

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