Problem 1. Social media users use a variety of devices to...

Problem 1. Social media users use a variety of devices to access social networking; mobile phones are increasingly popular. However, is there a difference in the various age groups in the proportion of social media users who use their mobile phone to access social networking? A study showed the following results for the different age groups, assume that 200 social media users for each age group were surveyed. Phone to Access | AGE social media | 18-34 | 35-64 | 65+ YES | 59% | 36% | 13% NO | 41% | 64% | 87%

Transcript

00:01 All right, so for this problem, to test if there is a difference, we'll be doing a kai squared test, where we take the sum of the differences between each observed value and each expected value, squared, divided by the expected value, where we have that the expected value for row i, column j, would be equal to the total across row i times the total across column j divided by the grand total now we're told that or basically we're given proportions here but we're also told that each age group had a sample size of 200 so we can find the observed frequencies and that's one key thing we always work with frequencies when we're talking about kye square distributions we can find the the observed frequencies by multiplying each one of these values by 200.

01:06 There we go.

01:08 And so we also don't need to figure out what the different column totals are because we know already the column totals will all be 200.

01:16 But we do need to find the first and second row totals just by adding up the observed frequencies across each.

01:23 So we have 118 plus 72 plus 26.

01:25 So 216 across the first row.

01:28 And then we have 82 plus 128 plus 174.

01:33 So 384 for the second row.

01:37 So what i'll do now, let's see, figure out the expected values for each one of these.

01:51 So one here, just going to make a couple of changes.

01:57 So for the expected value for row one column one, that's 216 times 200, divided by 200 times three, so divided by 600.

02:04 So the expected value would be 72.

02:08 Then we would actually have, because of the way that, the different values are repeated, we'd have the same expected value across each row.

02:18 For each row across each column, the expected value should be unchanging.

02:24 So then for the second row, we have that, the expected value should be 128 for each one.

02:41 So i'll do here, let's see...

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