Kerala Education Dept Report
Autor: iitkkapilm • September 7, 2015 • Term Paper • 1,838 Words (8 Pages) • 727 Views
QM-I Assignment Solution
Submitted by – Kapil Mathur (1411376), Section F
Solution to Problem #1(a)
Random samples of different sizes were generated from the given data in Excel using the RandBetween function.
For size n =6, the sampling distribution is shown in the figure below. Also, the sample size was incrementally increased and skewness and kurtosis were monitored to see when the sampling distribution was approximately normal. Based on the values tabulated below and the histograms shown, it can be concluded that the sampling distribution is approximately normal at n=33.
Sample size → | n =6 | n =18 | n =33 |
Mean | 21.6508 | 21.8647 | 21.7586 |
Std. Dev. | 2.3555 | 1.1964 | 0.9234 |
Skewness | -0.7693 | -0.1782 | 0.0618 |
Kurtosis | 1.2322 | 0.4679 | 0.1234 |
[pic 1]
[pic 2]
[pic 3]
Solution to Problem #1(b)
A simple random sample of size 60 was first drawn from the given data by stacking all the data in one column and using MINITAB’s ‘Random Data’ option.
Next, for stratified sampling, it was first identified that out of total 360 data points, Group A has 100, Group B has 90, Group C has 70, and Group D has 100 points. In other words, Group A & D have 27.78% of the total data points, Group B has 25% while Group C has 19.44%. Per the stratified sampling approach, samples should be drawn in the aforementioned proportion from each of the salary groups. Therefore, out of 60 following was the number of data points from each group:
Group A = 0.2778*60 = 16.68 → 17 points
Group B = 0.25*60 = 15 points
Group C = 0.1944*60 = 11.66 → 11 points
Group D = 0.2778*60 = 16.68 → 17 points
The simple random sample and the stratified sample are shown below along with their respective means and variances. I believe that stratified sampling is the better sampling method here because it gives you sample data that is more representative of the various segments existing in the population.
[pic 4][pic 5]
...