Answer :
Answer:
The standard error S.E of the mean is 5
Step-by-step explanation:
From the given data;
Fifty students are enrolled in a Business Statistics class.
After he first examination, a random sample of 5 papers was selected.
Now; let consider a random sample of 5 papers was selected. with the following grades : 60, 75, 80, 70, and 90
The objective of this question is to determine the standard error of the mean
In order to achieve this ; we need to find the mean and the standard deviation from the given data.
TO start with the mean;
Mean [tex]\overline X[/tex] = [tex]\dfrac{1}{n} \sum x_i[/tex]
Mean [tex]\overline X[/tex] = [tex]\dfrac{1}{5} (60+75+80+70+90)[/tex]
Mean [tex]\overline X[/tex] = 0.2(375)
Mean [tex]\overline X[/tex] = 75
On the other hand; the standard deviation is :
[tex]s = \sqrt{\dfrac{1}{n-1}\sum(x_i - \overline X)^2}[/tex]
[tex]s = \sqrt{\dfrac{1}{5-1}((60-75)^2+(75-75)^2+(80-75)^2+(70-75)^2+(90-75)^2 )}[/tex]
[tex]s = \sqrt{\dfrac{1}{4}(225+0+25+25+225 )}[/tex]
[tex]s = \sqrt{\dfrac{1}{4}(500 )}[/tex]
[tex]s = \sqrt{125}[/tex]
s = 11.18
Finally; the standard error S.E of the mean is:
[tex]S.E = \dfrac{s}{\sqrt{n}}[/tex]
[tex]S.E = \dfrac{11.18}{\sqrt{5}}[/tex]
[tex]S.E = \dfrac{11.18}{2.236}[/tex]
[tex]S.E = 5[/tex]
The standard error S.E of the mean is 5