Question

Below is a list of the profit or (loss) of 40 companies.

- Calculate the population parameters for all 40 companies profit or loss

- Select a sample of 10

- Calculate the point estimators of the sample

- Compare the results (Point estimators with Population Parameters)

$ In Millions

$9,862             $19,710          

$44,940           $48,351

$10,558           $5,070

$6,662             $3,033

$29,450           ($3,864)

7,602               $364.5

$9,195             $1,288

$2,679             $30,101           

$1,907             ($5786)

$4,078             $24,441

$2,463             $12,662

$8,630             $18,232

$4,517.4          $22,183

$8,197             $5,106

$3,842.8          $21,204

$4,065             $22,714

$2,997             $9,609

$246.5             $4,286

$3,577             $2,736

$2,421.9          $1,982

Answer 1

### Using Excel:

	Data	X-mu	(X-mu)^2
	9862	-653.33	426840.089
	9710	-805.33	648556.409
	44940	34424.67	1185057905
	48351	37835.67	1431537924
	10558	42.67	1820.7289
	5070	-5445.33	29651618.8
	6662	-3853.33	14848152.1
	3033	-7482.33	55985262.2
	29450	18934.67	358521728
	3864	-6651.33	44240190.8
	7602	-2913.33	8487491.69
	364.5	-10150.8	103039350
	9195	-1320.33	1743271.31
	1288	-9227.33	85143618.9
	2679	-7836.33	61408067.9
	30101	19585.67	383598469
	1907	-8608.33	74103345.4
	5786	-4729.33	22366562.2
	4078	-6437.33	41439217.5
	24441	13925.67	193924285
	2463	-8052.33	64840018.4
	12662	2146.67	4608192.09
	8630	-1885.33	3554469.21
	18232	7716.67	59546995.9
	4517.4	-5997.93	35975164.3
	22183	11667.67	136134523
	8197	-2318.33	5374653.99
	5106	-5409.33	29260851
	3842.8	-6672.53	44522656.6
	21204	10688.67	114247666
	4065	-6450.33	41606757.1
	22714	12198.67	148807550
	2997	-7518.33	56525286
	9609	-906.33	821434.069
	246.5	-10268.8	105448870
	4286	-6229.33	38804552.2
	3577	-6938.33	48140423.2
	2736	-7779.33	60517975.2
	2421.9	-8093.43	65503609.2
	1982	-8533.33	72817720.9
Total	420613.1		5233233045
Mean	10515.33

The population mean is given by:

The population standard deviation is given by:

## By using R command: We draw a random sample of size 10 from the given population.

> data=c(9862,9710,44940,48351,10558,5070,6662,3033,29450,3864,7602,364.5,9195,1288,2679,30101,1907,5786,4078 ,24441,2463 ,12662,8630 ,18232,4517.4,22183,8197,5106,3842.8,21204,4065 ,22714,2997,9609,246.5,4286,3577,2736,2421.9,1982)
> data
[1] 9862.0 9710.0 44940.0 48351.0 10558.0 5070.0 6662.0 3033.0 29450.0
[10] 3864.0 7602.0 364.5 9195.0 1288.0 2679.0 30101.0 1907.0 5786.0
[19] 4078.0 24441.0 2463.0 12662.0 8630.0 18232.0 4517.4 22183.0 8197.0
[28] 5106.0 3842.8 21204.0 4065.0 22714.0 2997.0 9609.0 246.5 4286.0
[37] 3577.0 2736.0 2421.9 1982.0
> x=sample(data,10)
> x
[1] 2463.0 12662.0 4517.4 4065.0 21204.0 5106.0 3033.0 9195.0 1288.0
[10] 8197.0

### By using excel:

	Sample(x)	(x-xbar)	(x-xbar)^2
	2463	-4710.04	22184477
	12662	5488.96	30128682
	4517.4	-2655.64	7052423.8
	4065	-3108.04	9659912.6
	21204	14030.96	196867839
	5106	-2067.04	4272654.4
	3033	-4140.04	17139931
	9195	2021.96	4088322.2
	1288	-5885.04	34633696
	8197	1023.96	1048494.1
Total	71730.4		327076431
xbar	7173.04

The sample mean is given by:

The sample standard deviation is given by:

From the point estimators of sample, the sample mean and sample standard deviation is smaller than the population parameter mean and standard deviation respectively.