1a. Describe one way in which you could randomly assign participants to an exper
ID: 3174680 • Letter: 1
Question
1a. Describe one way in which you could randomly assign participants to an experimental group or a control group. b.Explain the difference between the population and a sample in relation to a research study. c. Create a sampling distribution of the mean from the population of 1, 3, 5, 7, using a sample of size 2. Calculate the mean of the population and the mean of the sampling distribution. Do you get the same answer? Why or why not? Calculate the standard deviation of the population and the standard error of the sampling distribution. Do you get the same answer? Why or why not?
Explanation / Answer
X
1
3
5
7
Sample mean = 16 / 4 = 4
Now we get sample of size 2.
x1
x2
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
x14
x15
x16
1
3
5
7
1
3
5
7
1
3
5
7
1
3
5
7
1
1
1
1
3
3
3
3
5
5
5
5
7
7
7
7
x1
x2
x3
x4
x5
x6
x7
x8
x9
x10
x11
x12
x13
x14
x15
x16
1
3
5
7
1
3
5
7
1
3
5
7
1
3
5
7
1
1
1
1
3
3
3
3
5
5
5
5
7
7
7
7
x bar
1
2
3
4
2
3
4
5
3
4
5
6
4
5
6
7
Now we find mean of x bar
Mean of sample mean ( x bar ) = 64/16 = 4
Population mean and the sampling mean of the distributions are equal.
The sample mean is the unbiased estimator of the population mean so here we get the same answer.
X
1
3
5
7
SD =
2.2361
Population standard deviation is 2.2361
The standard error = 2.2361 / sqrt (16) = 0.559
Standard error and the population standard deviation are not the same.
Sample distribution is an unbiased estimator.
X
1
3
5
7
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