Compare the mean of the population to the mean of the...

Compare the mean of the population to the mean of the sampling distribution of the sample mean. Assume that random samples of size n = 2 are taken with replacement. Make sure to tell me the mean of the population , and the mean of the sampling distribution of the sample mean, .

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Transcript

00:01 Hey there, welcome to numerate.

00:03 We are asked to calculate the mean and variance of the above population shown as five values here.

00:12 So this is part a.

00:14 We're going to calculate the variance first.

00:17 I'm sorry, the mean first.

00:19 So the mean is going to be represented as mu, the population mean, taking account the sum of all our values divided by n.

00:27 So if we sum of all of our values here, we have 916, we have 25, divided by our sample size, which is 5, so therefore our mean should equal 5.

00:47 Perfect.

00:50 So for part b, part b, what we have here is list all the possible values of n equals 2 without replacement, where the order is not important and list the sample mean.

01:03 So let's start with the possible samples.

01:10 Possible samples.

01:19 We're going to start with one.

01:20 So we have one, three.

01:29 We have one five and one seven.

01:42 Okay, and then one nine.

01:48 And then now we're going to move on to the three.

01:51 So what we have here is three, five, three seven, and three nine.

02:06 And now we're going to move on to fives, which is five, seven, five, nine.

02:20 And then now we have seven, which remains as seven nine.

02:28 All right, so these are the possible samples here with our sample size as equaling to...