PPT - Test for two independent samples.pptx

independent samples

1. Test for two independent samples By: Stephanie M. Trangia

2. Example Within a school district, students were randomly assigned to one of two Math teachers - Mrs. Smith and Mrs. Jones. After the assignment, Mrs. Smith had 28 students, and Mrs. Jones had 25 students. At the end of the year, each class took the same standardized test. Mrs. Smith's students had an average test score of 78, with a standard deviation of 10; and Mrs. Jones' students had an average test score of 85, with a standard deviation of 15. Test the hypothesis that Mrs. Smith and Mrs. Jones are equally effective teachers. Use a 0.10 level of significance. (Assume that student performance is approximately normal. Assuming that the population variances are equal)

3. solution What is the null hypothesis? - ( This implies that Mrs. Smith and Mrs. Jones are equally effective teachers) What is the alternative hypothesis? - (This implies that Mrs. Smith and Mrs. Jones are not equally effective teachers)  

4. Solution What is the test statistic to be used? Case 3 is used since the population standard deviation are unknown, and the sample sizes are lesser than 30, also, the population standard deviation are assumed to be equal.  

5. solution What is the appropriate critical region? or or Note: The value of the critical value refers to two-tailed test, with the degrees of freedom referring 60, which is closer to 51.  

6. Solution The Shaded area is the critical region area

7. solution What is the actual value of the test statistic?  

8. Solution Statistical Decision True or False, Implies true Reject the Null Hypothesis    

9. Graphically

10. solution What is the statistical conclusion? - Therefore, we do have sufficient evidence to conclude that, Mrs. Smith and Mrs. Jones are not equally effective teachers at .  

11. Another example Maya, a restaurant owner, wants to test if her two managers perform at the same level. To do that, she collects data about the number of customer complaints at two random samples of shifts (one for each manager). Here is a summary of the results: Mio wants to use these results to carry out a two-sample t-test to determine if the mean numbers of complaints are significantly different for the two managers. Use 0.05 level of significance.   Manager A Manager B Mean 4 complaints 5 complaints Standard Deviation 0.3 complaints 0.5 complaints Number of shifts 33 31

12. solution What is the null hypothesis? - ( This implies that two managers on the average have equal performance level) What is the alternative hypothesis? - ( This implies that two managers on the average do not have equal performance level )  

13. Solution What is the test statistic to be used? Case 2 is used since the population standard deviation are unknown, and the sample sizes are greater than 30.  

14. solution What is the appropriate critical region? or or or  

15. Solution The Shaded area is the critical region area

16. solution What is the actual value of the test statistic?     Manager A Manager B Mean 4 complaints 5 complaints Standard Deviation 0.3 complaints 0.5 complaints Number of shifts 33 31

17. solution What is the appropriate critical region? or True or False, Implies True, reject the Null Hypothesis  

18. Graphically

19. solution What is the statistical conclusion? - Therefore, we do have sufficient evidence to conclude that, the two managers differs in their performance level at 0.05 level of significance.