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Two Sample Tests
In some situation the researchers may be taking statistical decisions based on two samples. Each of the two samples may represent a particular under consideration. For example one may be interested to study the effectiveness of teaching methods like unstructured teaching and structured teaching. Suppose college have changed their method of teaching from unstructured teaching to structured teaching recently. Then the researcher has to take a random sample of students of a particular programme from different colleges and collect their performances before introducing the structured methods of teaching and after introducing the structured method of teaching. The respective observation will form two samples .
There are many more examples which are as listed below:
a.Number of defects found in the daily lots of items produced by a set of similar machines before and after installing a costly automatic inspection systems in them.
b. Monthly sales revenues of a product in different regions before launching an advertisement campaign and after launching the advertisement campaign.
c.Number of daily transaction in a bank before and after introducing computers.
d. Number of outpatients treated in a government hospital before and after providing modern infrastructure.
There are various non parametric tests but we will discuss only a few of the better known and more widely used ones.
a.The sign test
1. One samples test
2.Two sample sign test ( sing test for paired data)
3.A rank sum test ( Mann Whitney u test)
4. The one sample runs test
5.Rank correlation ( described in chapter 10 )
Regression Line The line of regression is the line which give the best estimate to the values of one variable for any specific values of other variable. For t
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a. What do you mean by linear programming problem? Explain the steps involved in linear programming problem formulation? b. A paper mill produces two grades of paper viz., X and Y.
Example 2 Max Z = 3x 1 - x 2 Subject to 2x 1 + x 2 ≥ 2 x 1 + 3x 2 ≤ 3 x 2 ≤ 4 & x 1 ≥ 0, x 2 ≥ 0 A
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ONE SAMPLE RUNS TEST A number of methods have been developed fro judging the randomness of samples on the basis of the order in which teh observations are taken. It is
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