In: Statistics and Probability
I am going to study gender differences and scores on the spelling test. Ind variable: Gender (Male or female) Dep variable: spelling test score Null: There is no difference between males and females on the spelling test. Directional: Boys will score higher than girls on the spelling test. Now, create a study.
Creating study-
At first we perform a study taking spelling test of 15 students of our class. Our of 20 the scores are as follows.
Boy | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
Score | 18 | 17 | 19 | 12 | 17 | 19 | 18 | 16 | 15 |
Girl | 1 | 2 | 3 | 4 | 5 | 6 | |||
Score | 12 | 20 | 15 | 13 | 12 | 14 |
Hypothesis test-
Suppose, random variables X and Y denote scores on the spelling test of males and females respectively.
We have to test for null hypothesis
against the alternative hypothesis
Our test statistics is given by
Here,
First sample size
Second sample size
Degrees of freedom
[Using R-code '1-pt(1.815008,13)']
We reject our null hypothesis if , level of significance.
We generally test for level of significance 0.10, 0.05 or something like these.
So, we can reject our null hypothesis.
Hence, based on the given data we can conclude that boys score significantly higher than girls on the spelling test.