A 2012 pew research survey asked 2373 randomly sampled...

A 2012 Pew Research survey asked 2373 randomly sampled registered voters their political affiliation (Republican; Democrat; Independent) and whether or not they identify as swing voters. 35% of respondents identified as Independent; 23% identified as swing voters and 11% identified as both. Are identifying as an Independent and identifying as a swing voter mutually exclusive? Explain. What percent of voters identify as Independent but not as swing voters? What percent of voters identify as Independent or as a swing voter? What percent of voters do not identify as either an Independent or swing voter? Are identifying as an Independent and identifying as a swing voter independent? Explain.

Transcript

00:01 So to begin here, i'll note that we don't actually need to completely fill out this table to be able to answer.

00:07 But we know that the overall total number of people sampled was 2 ,373.

00:16 And we know that 35 % of the respondents identified as independent.

00:22 So the column total for independence is 0 .35 times 2373 is going to be roughly 870 .8 ,000.

00:34 31, we have that 23 identify as, or identified as, or pardon me, 23 % identified as swing voters.

00:44 So 0 .23 times 2373 equals roughly 546.

00:51 And we know that 1 ,190 identified as both, 1 ,190.

01:00 Or pardon me, i just realized i put those in the wrong categories there, so that should be 546 here.

01:05 Then.

01:10 Okay, i think i found it.

01:12 Doing a little bit of digging online, it's not that 1 ,190 identified as both.

01:17 It's at 11 % identified as both.

01:21 So that should be roughly 261 in the intersection of the two events.

01:30 So, that being said, for the first part of the problem, or i'll call that part a, we're asked if being independent and being a swing voter are mutually excluded.

01:40 Well, if i'll just say i and s for being independent and being a swing voter were mutually exclusive, m .e.

01:52 For short, then we would have that the number of things in the intersection of independent and swing voter must be equal to zero, which is not the case.

02:07 We can see that it equals 261, therefore, they are not mutually exclusive.

02:17 For the second part of the problem here, part b, we're asked what percent of voters identify as independent but not swing voters? so we're asked for the proportion of independent and the complement of swing.

02:31 So that would be equal to the proportion of independent minus the proportion of independent and swing.

02:40 So we know that the proportion of voters who identified as independent was 0 .35.

02:48 The proportion who identified as independent and swing voters was 0 .11.

02:53 So the proportion of independent and not swing would have to be 0 .24.

02:59 For part c, we're looking for the proportion who identify as independent or as a swing voter...

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