The document discusses how to conduct an independent samples t-test to compare the means of two samples. Specifically: 1. The null hypothesis is that the means of the two classes (Class A and B) are equal. The alternative hypothesis is that they are not equal. 2. With a significance level of 0.05, the test statistic is calculated to be -0.67. 3. Based on the decision rule, the null hypothesis is not rejected, meaning there is no significant difference between the test performances of Class A and Class B.

1. T-test for
Independent
Sample
EDELIZA R. TAGACAY
BATCH 4-MIT

2. Independent Samples T-test
An independent samples t-test evaluates whether two means from two samples of the same
dependent variable are significantly different from one another.
An independent samples t-test is used only with interval or ratio data not nominal nor ordinal

3. A statistics teacher wants to compare his two classes to see if they
performed any differently on the tests he gave that semester. Class A had 25
students with an average score of 70, standard deviation 15. Class B had 20
students with an average score of 74, standard deviation 25. Using alpha 0.05, did
these two classes perform differently on the tests?
Sample:
1. Define Null and Alternative Hypotheses
2. State Alpha
3. Calculate Degrees of Freedom
4. State Decision Rule
5. Calculate Test Statistic
6. State Results
7. State Conclusion

4. A statistics teacher wants to compare his two classes to see if they
performed any differently on the tests he gave that semester. Class A had 25
students with an average score of 70, standard deviation 15. Class B had 20
students with an average score of 74, standard deviation 25. Using alpha 0.05, did
these two classes perform differently on the tests?
Sample:
1. Define Null and Alternative Hypotheses
H0; µ classA= µ ClassB
H1; µ classA≠ µ ClassB

5. A statistics teacher wants to compare his two classes to see if they
performed any differently on the tests he gave that semester. Class A had 25
students with an average score of 70, standard deviation 15. Class B had 20
students with an average score of 74, standard deviation 25. Using alpha 0.05, did
these two classes perform differently on the tests?
Sample:
2. State Alpha
α=0.05

6. A statistics teacher wants to compare his two classes to see if they
performed any differently on the tests he gave that semester. Class A had 25
students with an average score of 70, standard deviation 15. Class B had 20
students with an average score of 74, standard deviation 25. Using alpha 0.05, did
these two classes perform differently on the tests?
Sample:
3. Calculate Degrees of Freedom
Degrees of Freedom for Independent Samples t-Test
df = (n1 – 1) + (n2 – 1)
df = (25 – 1) + (20 – 1)=43

7. A statistics teacher wants to compare his two classes to see if they
performed any differently on the tests he gave that semester. Class A had 25
students with an average score of 70, standard deviation 15. Class B had 20
students with an average score of 74, standard deviation 25. Using alpha 0.05, did
these two classes perform differently on the tests?
Sample:
4. State Decision Rule

8. 2.0167
Critical
Value

9. A statistics teacher wants to compare his two classes to see if they
performed any differently on the tests he gave that semester. Class A had 25
students with an average score of 70, standard deviation 15. Class B had 20
students with an average score of 74, standard deviation 25. Using alpha 0.05, did
these two classes perform differently on the tests?
Sample:
4. State Decision Rule
2.0167
-2.0167
If t is less than -2.0167, or greater than 2.0167, reject the null hypothesis.

10. A statistics teacher wants to compare his two classes to see if they performed any differently on
the tests he gave that semester. Class A had 25 students with an average score of 70, standard deviation 15.
Class B had 20 students with an average score of 74, standard deviation 25. Using alpha 0.05, did these two
classes perform differently on the tests?
Sample:
5. Calculate Test Statistic

11. A statistics teacher wants to compare his two classes to see if they performed any differently on
the tests he gave that semester. Class A had 25 students with an average score of 70, standard deviation 15.
Class B had 20 students with an average score of 74, standard deviation 25. Using alpha 0.05, did these two
classes perform differently on the tests?
Sample:
5. Calculate Test Statistic

12. A statistics teacher wants to compare his two classes to see if they performed any differently on
the tests he gave that semester. Class A had 25 students with an average score of 70, standard deviation 15.
Class B had 20 students with an average score of 74, standard deviation 25. Using alpha 0.05, did these two
classes perform differently on the tests?
Sample:
6. State Results
Decision Rule:
If t is less than -2.0167, or greater than 2.0167, reject the null
hypothesis.
t=-0.67
Result: Do not reject H0

13. A statistics teacher wants to compare his two classes to see if they performed any differently on
the tests he gave that semester. Class A had 25 students with an average score of 70, standard deviation 15.
Class B had 20 students with an average score of 74, standard deviation 25. Using alpha 0.05, did these two
classes perform differently on the tests?
Sample:
7. State Conclusion
There was no significant difference between the test performances of
Class A and Class B, t=-0.67, p>0.05

14. Thank You!
CTTO