The file IUSalariestxt contains the salaries of a random sam

The file IUSalaries.txt contains the salaries of a random sample of 50 IU Bloomington faculty,
along with the salaries of a random 50 IU athletics employees.

\"Job\" \"Salary\"
\"Faculty\" 102416
\"Faculty\" 56333
\"Faculty\" 52934
\"Faculty\" 152893
\"Faculty\" 51090
\"Faculty\" 87998
\"Faculty\" 106930
\"Faculty\" 72500
\"Faculty\" 111628
\"Faculty\" 90945
\"Faculty\" 63500
\"Faculty\" 96593
\"Faculty\" 113825
\"Faculty\" 66086
\"Faculty\" 12565
\"Faculty\" 29088
\"Faculty\" 79698
\"Faculty\" 72828
\"Faculty\" 54631
\"Faculty\" 184296
\"Faculty\" 83209
\"Faculty\" 80937
\"Faculty\" 80123
\"Faculty\" 154000
\"Faculty\" 111180
\"Faculty\" 41820
\"Faculty\" 82430
\"Faculty\" 70000
\"Faculty\" 67170
\"Faculty\" 101536
\"Faculty\" 81723
\"Faculty\" 307668
\"Faculty\" 72930
\"Faculty\" 90000
\"Faculty\" 51425
\"Faculty\" 50245
\"Faculty\" 53987
\"Faculty\" 105305
\"Faculty\" 31761
\"Faculty\" 140273
\"Faculty\" 66900
\"Faculty\" 45900
\"Faculty\" 99000
\"Faculty\" 121190
\"Faculty\" 40216
\"Faculty\" 69750
\"Faculty\" 128312
\"Faculty\" 168943
\"Faculty\" 51201
\"Faculty\" 72500
\"Athletics\" 21107
\"Athletics\" 40800
\"Athletics\" 65000
\"Athletics\" 39814
\"Athletics\" 47861
\"Athletics\" 28434
\"Athletics\" 208539
\"Athletics\" 59022
\"Athletics\" 24480
\"Athletics\" 39541
\"Athletics\" 215701
\"Athletics\" 34272
\"Athletics\" 168300
\"Athletics\" 31824
\"Athletics\" 16084
\"Athletics\" 604858
\"Athletics\" 43410
\"Athletics\" 54060
\"Athletics\" 71400
\"Athletics\" 98838
\"Athletics\" 30805
\"Athletics\" 24149
\"Athletics\" 49939
\"Athletics\" 41820
\"Athletics\" 28267
\"Athletics\" 122400
\"Athletics\" 37170
\"Athletics\" 215701
\"Athletics\" 51154
\"Athletics\" 43697
\"Athletics\" 86626
\"Athletics\" 56100
\"Athletics\" 35714
\"Athletics\" 40810
\"Athletics\" 46818
\"Athletics\" 51000
\"Athletics\" 89573
\"Athletics\" 178500
\"Athletics\" 15267
\"Athletics\" 105000
\"Athletics\" 40522
\"Athletics\" 100717
\"Athletics\" 53040
\"Athletics\" 35714
\"Athletics\" 87277
\"Athletics\" 107100
\"Athletics\" 36683
\"Athletics\" 109936
\"Athletics\" 25210
\"Athletics\" 52530

Do IU Blo omington faculty and IU Athletics employees have the same distribution of salaries?
Explain (preferable in R code)

Solution

Here we have given that The file IUSalaries.txt contains the salaries of a random sample of 50 IU Bloomington faculty, along with the salaries of a random 50 IU athletics employees.

Do IU Blo omington faculty and IU Athletics employees have the same distribution of salaries?

Faculty is denoted by 1

and Athletics is denoted by 0

This we can done by using Kolmogorov-Smirnov test.

First we make two data sets one as faculty and second as salary.

Data Set 1:

100 data points were entered

Mean = 0.5000

95% confidence interval for actual Mean: 0.4003 thru 0.5997

Standard Deviation = 0.503

High = 1.00 Low = 0.00

Third Quartile = 1.00 First Quartile = 0.00

Median = 0.5000

Average Absolute Deviation from Median = 0.500

KS says it\'s unlikely this data is normally distributed: P= 0.00 where the normal distribution has mean= 0.5379 and sdev= 0.3750

Items in Data Set 1:

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00

Data Set 2:

100 data points were entered

Mean = 8.2930E+04

95% confidence interval for actual Mean: 6.8443E+04 thru 9.7417E+04

Standard Deviation = 7.301E+04

High = 6.049E+05 Low = 1.257E+04

Third Quartile = 1.013E+05 First Quartile = 4.182E+04

Median = 6.6493E+04

Average Absolute Deviation from Median = 4.103E+04

John Tukey defined data points as outliers if they are 1.5*IQR above the third quartile or below the first quartile.

Following Tukey, the following data points are outliers: 6.049E+05 3.077E+05 2.157E+05 2.157E+05 2.085E+05

KS says it\'s unlikely this data is normally distributed: P= 0.00 where the normal distribution has mean= 1.5620E+05 and sdev= 1.1861E+05

KS is not particularly happy calling this data log normally distributed: P= 0.20 where the log normal distribution has geometric mean= 7.0036E+04 and multiplicative sdev= 2.100

Items in Data Set 2:

1.257E+04 1.527E+04 1.608E+04 2.111E+04 2.415E+04 2.448E+04 2.521E+04 2.827E+04 2.843E+04 2.909E+04 3.081E+04 3.176E+04 3.182E+04 3.427E+04 3.571E+04 3.571E+04 3.668E+04 3.717E+04 3.954E+04 3.981E+04 4.022E+04 4.052E+04 4.080E+04 4.081E+04 4.182E+04 4.182E+04 4.341E+04 4.370E+04 4.590E+04 4.682E+04 4.786E+04 4.994E+04 5.025E+04 5.100E+04 5.109E+04 5.115E+04 5.120E+04 5.143E+04 5.253E+04 5.293E+04 5.304E+04 5.399E+04 5.406E+04 5.463E+04 5.610E+04 5.633E+04 5.902E+04 6.350E+04 6.500E+04 6.609E+04 6.690E+04 6.717E+04 6.975E+04 7.000E+04 7.140E+04 7.250E+04 7.250E+04 7.283E+04 7.293E+04 7.970E+04 8.012E+04 8.094E+04 8.172E+04 8.243E+04 8.321E+04 8.663E+04 8.728E+04 8.800E+04 8.957E+04 9.000E+04 9.095E+04 9.659E+04 9.884E+04 9.900E+04 1.007E+05 1.015E+05 1.024E+05 1.050E+05 1.053E+05 1.069E+05 1.071E+05 1.099E+05 1.112E+05 1.116E+05 1.138E+05 1.212E+05 1.224E+05 1.283E+05 1.403E+05 1.529E+05 1.540E+05 1.683E+05 1.689E+05 1.785E+05 1.843E+05 2.085E+05 2.157E+05 2.157E+05 3.077E+05 6.049E+05

The two data dets are not having same distribution one have normal distribution and other has log normal distribution.