T-Test in Statistics

T-TEST Cabral, MarthaBarreras, GladysCastro, ElanieDelmar, Fatima

What is a T-Test?• Used to test hypothesis

about means when the population variance is unknown.

• Used when n<30• Introduced in 1908 by

William Gosset to monitor the quality of stout.

Variances of T-Test• Single

sample/comparison between population mean & sample mean

• Independent samples• Dependents sample/two

correlated means

Uses of T-testarticle

hypothesis

statistical tools/treatment

summary of the findings

Steps in Hypothesis Testing1. Formulate the two hypothesis: Ho

& HA2. Select the level of significance &

tailed test: one-tailed test or two-tailed test?

3. Determine the test statistic4. Compute for the acceptance

region/value of statistic5. Compute for the rejection region:

degree of freedom & critical value6. Formulate your findings and

decision7. Conclusion

Single Sample T-Test

sample mean

population mean

standard deviation

sample size

Single Sample T-Test Example For many semesters, Professor Snape has recorded his students’ grades are 83. His current class of 28 students seems to be better than average in ability and she wants to show that according to their average “the current class is superior than the previous classes”. Do the class mean of 86.2 and standard deviation of 12, present sufficient evidence to support her claim that the current class is superior? Use 5% level of significance.

Single Sample T-Test Example

The average family size in the Philippines was reported as 4.25. A random of families in a particular street resulted in the following family sizes: 5, 6, 7, 4, 3, 8, 2 and 9. At 0.10 significance level, does the average family size more than the national average?

Independent Sample T-Test

means

sample sizes

variances

Independent Sample T-Test Example A college graduate is trying to decide whether to pursue a Master’s Degree or not. He will only do so if he is convinced that Master’s degree holders loan more than college graduates. The yearly salaries were P170, 000 and P126, 000 respectively with corresponding standard deviations of P6, 000 and P5, 400. Using 10% significance level, should he pursue a higher degree?

Independent Sample T-Test Example Previous midterm examination in Statistics showed an average score obtained by students in section A and B are the same. The department chair randomly selects two sections of statistics classes to record the performance of the students.

Is there an evidence to say by the department chair that the scores in Section A & B are the same? Use 5% significance level

Sections No. of students

Means Variances

A 15 85.2 10.40B 14 86.1 20.99

Dependent Sample T-Test mean difference

standard deviation of differences

sample

Dependent Sample T-Test Example The following data are the score of the students in the pre-test and post-test in statistics. Can we say that the students understand most of the topics in statistics at 5% level of significance?

ObservationsPre-test 6 7 5 5 4 9 2 2 3 6 Post-test 9 11 8 5 6 3 7 9 10 9

Dependent Sample T-Test Example It is of interest to compare the scores of 10 players in archery. Thus, at 5% level of significance, we can say that there is a positive difference between the scores of the students between post-test and pre-test in Statistics.Game Number

Players’ Scores

1 77 84 73 65 92 49 58 67 85 96

2 102 85 70 79 84 57 69 82 49 99