In: Math

# Below is a list of the profit or (loss) of 40 companies. - Calculate the population...

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

## Solutions

##### Expert Solution

### 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
 9862.0 9710.0 44940.0 48351.0 10558.0 5070.0 6662.0 3033.0 29450.0
 3864.0 7602.0 364.5 9195.0 1288.0 2679.0 30101.0 1907.0 5786.0
 4078.0 24441.0 2463.0 12662.0 8630.0 18232.0 4517.4 22183.0 8197.0
 5106.0 3842.8 21204.0 4065.0 22714.0 2997.0 9609.0 246.5 4286.0
 3577.0 2736.0 2421.9 1982.0
> x=sample(data,10)
> x
 2463.0 12662.0 4517.4 4065.0 21204.0 5106.0 3033.0 9195.0 1288.0
 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.

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