Question

Fifty students are enrolled in a Business Statistics class. After the first examination, a random sample of 5 papers was selected. The grades were 60, 75, 80, 70, and 90. a) Determine the standard error of the mean

Answer 1

The standard error S.E of the mean is 5

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
`\overline X` =
`(1)/(n) \sum x_i`

Mean
`\overline X` =
`(1)/(5) (60+75+80+70+90)`

Mean
`\overline X` = 0.2(375)

Mean
`\overline X` = 75

On the other hand; the standard deviation is :

`s = \sqrt{(1)/(n-1)\sum(x_i - \overline X)^2}`

`s = \sqrt{(1)/(5-1)((60-75)^2+(75-75)^2+(80-75)^2+(70-75)^2+(90-75)^2 )}`

`s = \sqrt{(1)/(4)(225+0+25+25+225 )}`

`s = \sqrt{(1)/(4)(500 )}`

`s = √(125)`

s = 11.18

Finally; the standard error S.E of the mean is:

`S.E = (s)/(√(n))`

`S.E = (11.18)/(√(5))`

`S.E = (11.18)/(2.236)`

`S.E = 5`

The standard error S.E of the mean is 5