Question

The following data represent a sample of the assets (in millions of dollars) of 28 credit unions in a state. Assume that the population in this state is normally distributed with σ=3.5 million dollars. Use Excel to find the 99% confidence interval of the mean assets in millions of dollars. Round your answers to three decimal places and use ascending order.

Assets
12.23
2.89
13.19
73.25
11.59
8.74
7.92
40.22
5.01
2.27
16.56
1.24
9.16
1.91
6.69
3.17
4.78
2.42
1.47
12.77
4.39
2.17
1.42
14.64
1.06
18.13
16.85
21.58

Provide your answer below:        (    ,    )

Answer 1

Solution:

We are given that a sample of the assets (in millions of dollars) of 28 credit unions in a state. The population in this state is normally distributed with σ =3.5 million dollars.

We have to use Excel to find the 99% confidence interval of the mean assets in millions of dollars.

Formula:

where is the sample mean and E = Margin of Error for which we will use Excel commands:

	12.23
	2.89
	13.19
	73.25
	11.59
	8.74
	7.92
	40.22
	5.01
	2.27
	16.56
	1.24
	9.16
	1.91
	6.69
	3.17
	4.78
	2.42
	1.47
	12.77
	4.39
	2.17
	1.42
	14.64
	1.06
	18.13
	16.85
	21.58
=AVERAGE( SELECT DATA RANGE)	11.347
=CONFIDENCE.NORM(alpha, SD, n )	1.704

For =AVERAGE( SELECT DATA RANGE) , we select all numbers entered in excel.

which gives answer = 11.347

Thus sample mean =

For =CONFIDENCE.NORM(alpha, SD, n) ,

we use alpha = 1 - c = 1 - 0.99 = 0.01 , SD = Standard Deviation = 3.5 and Size = n = 28.

That is:

=CONFIDENCE.NORM( 0.01 , 3.5 , 28 )

=1.704

Thus E = 1.704

Thus a 99% confidence interval for mean is: