An observational study is conducted to ninety students, male and female in Computer Secretarial vocational course. They are given a test in psychomotor skills through basic typing. There scores are classified into high and low using the Chi – Square Test of Independence in One sample, Two criterion variables at 0.05 level of significance. Another study is a survey of spelling performance of ten male and ten female students in grade 5 elementary students. The objective is to test the null hypothesis that there is no significant difference between the performance of male and female students in the spelling test using the t – Test for Independent Samples at 0.05 level of significance.
- t – Test for Independent Samples
Problem:
Is there a significant difference between the performance of male and female students in spelling?
Hypotheses:
H0 : There is no significant difference between the performance of grade 5 male and female student in spelling.
H1 : There is a significant difference between the performance of grade 5 male and female student in spelling.
Level of Significance:
α =0.05
df = n1+n2-2 =18
t0.05=1.734 Tabular value
Statistics:
t – Test for Independent Samples
Decision Rule:
If the t – computed value is greater than or beyond the t – tabular or critical value, reject the null hypothesis, H0.
Conclusion:
Since the t – computed value of 2.88 is greater than the t – tabular value of 1.734 at 0.05 level of significance with 18 degree of freedom, the null hypothesis is rejected in favor of the research hypothesis, H1. this means that there is a significant difference between the performance of grade 5 male and female student in spelling. It implies that the grade 5 male students perform better than the grade 5 female students considering that the mean or average score of the grade 5 male students of 13.1 is greater compared to the average of the grade 5 female students of 7.8 only.
- Chi – Square Test of Independence in One sample, Two criterion variables
Is there a significant relationship between sex and scores in psychomotor skill in basic typing?
Hypotheses:
H0 : There is no significant relationship between sex and scores in psychomotor skill in basic typing.
H1 : There is a significant relationship between sex and scores in psychomotor skill in basic typing.
Level of Significance:
α =0.05
df=c-1r-1=1
X0.052=3.84 Tabular value
Statistics:
X2 , Chi – Square Test of Independence in One sample, Two criterion variables
Decision Rule:
If the X2 – computed value is greater than or beyond the X2 – tabular or critical value, reject the null hypothesis, H0.
Conclusion:
The X2 computed value of 10.292 is greater than the X2 tabular value of 3.84 at 0.05 level of significance with one degree of freedom. This leads to the confirmation of the research hypothesis, H1, which means that a significant relationship exists between sex and score in psychomotor skill in basic typing. It implies that the female’s high scores are more in psychomotor skills than the male counterpart is.
Appendices
- t – Test for Independent Samples
Male Female
Solution:
- solve for the sum of the square of each sample
SS1=X12-(X1)2n1
=1891-(131)210
=174.9
SS2=X22-(X2)2n2
=738-78210
=129.6
- solve t
t=X1-X2SS1+SS2n1+n2-21n1+1n2
Substitute the respective values,
t=2.88
- Chi – Square Test of Independence in One sample, Two criterion variables
Solution:
- For expected values: multiply the column total to the row total and divide the product by the grand total.
In detail,
50x4690=25.56
50x4490=24.44
40x4690=20.44
40x4490=19.56
- Solve for X2
X2=(O-E)2E Where O is the observe data and E is the expected data
Substitute the respective values,
X2=10.292
