8. Which of the following is a plausible representation of...

8. Which of the following is a plausible representation of the sampling distribution of sample proportions given that the sample size is 30? Show your calculations and/or provide a clear explanation. A Frequency of sample_proportion 200 160 120 80 40 0.2 0.4 0.6 0.8 1.0 sample_proportion mean (p?) = 0.497741 B Frequency of sample_proportion 350 300 250 200 150 100 50 0.2 0.4 0.6 0.8 1.0 sample_proportion mean (p?) = 0.62133 C Frequency of sample_proportion 300 250 200 150 100 50 0.2 0.4 0.6 0.8 1.0 sample_proportion mean (p?) = 0.62199 D Frequency of sample_proportion 180 160 140 120 100 80 60 40 20 0.2 0.4 0.6 0.8 1.0 sample_proportion mean (p?) = 0.619294

Transcript

00:01 So before i get to the answers here, let's remind ourselves what's going on.

00:04 So first of all, we have n is equal to 30, which tells us that the central limit theorem applies, right? the central limit theorem is one of the holy grails of statistics.

00:15 And the central limit theorem tells us what the sampling distribution is, right? the central limit tells us that the sampling distribution of the mean, right, the sampling distribution of x bar, is normal with the true underlying mean, mu, and sigma over root n, right? this is what the central limit theorem says.

00:43 And in particular, we know something about what the normal distribution looks like, right? it will be normal, right? whenever you have a big sample size, the sampling distribution will be normal.

00:55 And if it's normal, that means it will be symmetric, right? and bell -shaped, right? the normal distribution looks like, well, that's not my best normal distribution, like that, right? it's got that symmetric bell -shaped look to it.

01:15 So here, i would immediately start rejecting some of these distributions for being skewed, right? if i look at b, b to me looks right skewed.

01:30 You see that it's not symmetric around the mean, the whole idea of the normal distribution that is symmetric, left and right.

01:39 So i don't buy that b would be plausible, right? similarly, you can see for a, it's got the wrong mean.

02:03 It looks to me like, right, if the true, if true proportion is 0 .6, proportion is equal to 0 .6 proportion.

02:17 And in this case, it looks like a 0 .62 because b, c, and d are all centered around 0 .62.

02:25 You know that a is just located at the wrong place, right? a looks kind of symmetric, but a is simply at the wrong place...

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