1. Slide 12- 1 Copyright © 2010, 2007, 2004 Pearson Education, Inc. All Rights Reserved. Active Learning Lecture Slides For use with Classroom Response Systems Elementary Statistics Eleventh Edition and the Triola Statistics Series by Mario F. Triola Chapter 12: Analysis of Variance

2. Slide 12- 2 Copyright © 2010, 2007, 2004 Pearson Education, Inc. All Rights Reserved. Given the Minitab display below, assume you want to use a 0.05 significance level in testing the null hypothesis that the different samples come from populations with the same mean. Identify the test statistic: A. 13.500 B. 5.17 C. 4.500 D. 0.011 SourceDFSSMSFP Factor 313.5004.5005.170.011 Error 1613.9250.870 Total 1927.425

3. Slide 12- 3 Copyright © 2010, 2007, 2004 Pearson Education, Inc. All Rights Reserved. Given the Minitab display below, assume you want to use a 0.05 significance level in testing the null hypothesis that the different samples come from populations with the same mean. Identify the test statistic: A. 13.500 B. 5.17 C. 4.500 D. 0.011 SourceDFSSMSFP Factor 313.5004.5005.170.011 Error 1613.9250.870 Total 1927.425

4. Slide 12- 4 Copyright © 2010, 2007, 2004 Pearson Education, Inc. All Rights Reserved. Given the Minitab display below, assume you want to use a 0.05 significance level in testing the null hypothesis that the different samples come from populations with the same mean. What can you conclude about the equality of the population means? A.Accept the null hypothesis since the p-value is less than the significance level. B.Accept the null hypothesis since the p-value is greater than the significance level. C.Reject the null hypothesis since the p-value is greater than the significance level. D.Reject the null hypothesis since the p-value is less than the significance level. SourceDFSSMSFP Factor 313.5004.5005.170.011 Error 1613.9250.870 Total 1927.425

5. Slide 12- 5 Copyright © 2010, 2007, 2004 Pearson Education, Inc. All Rights Reserved. Given the Minitab display below, assume you want to use a 0.05 significance level in testing the null hypothesis that the different samples come from populations with the same mean. What can you conclude about the equality of the population means? A.Accept the null hypothesis since the p-value is less than the significance level. B.Accept the null hypothesis since the p-value is greater than the significance level. C.Reject the null hypothesis since the p-value is greater than the significance level. D.Reject the null hypothesis since the p-value is less than the significance level. SourceDFSSMSFP Factor 313.5004.5005.170.011 Error 1613.9250.870 Total 1927.425

6. Slide 12- 6 Copyright © 2010, 2007, 2004 Pearson Education, Inc. All Rights Reserved. The following results are from a statistics package in which all of the F values and P-values are given. Determine if there is a significant effect from the interaction. SourceDFSSMSFP A 2415.87305207.936521.88259.1637 B 32997.47186999.157299.04603.0001 Interaction 6707.26626117.877711.06723.3958 Error 465080.81667110.45254 Total 579201.42784 A.Reject the null hypothesis that there is no effect due to the interaction. B.Fail to reject the null hypothesis that there is no effect due to the interaction.

7. Slide 12- 7 Copyright © 2010, 2007, 2004 Pearson Education, Inc. All Rights Reserved. The following results are from a statistics package in which all of the F values and P-values are given. Determine if there is a significant effect from the interaction. SourceDFSSMSFP A 2415.87305207.936521.88259.1637 B 32997.47186999.157299.04603.0001 Interaction 6707.26626117.877711.06723.3958 Error 465080.81667110.45254 Total 579201.42784 A.Reject the null hypothesis that there is no effect due to the interaction. B.Fail to reject the null hypothesis that there is no effect due to the interaction.

8. Slide 12- 8 Copyright © 2010, 2007, 2004 Pearson Education, Inc. All Rights Reserved. The following Minitab display results from a study in which three different teachers taught calculus classes of five different sizes. The class average was recorded for each class. Assuming no effect from interaction between teacher and class size, test the claim that the teacher has no effect on the class average. A.Reject the null hypothesis that the teacher has no effect on class size. B.Fail to reject the null hypothesis that the teacher has no effect on class size. SourceDFSSMSF P Teacher 256.9328.471.0180.404 Class Size 4672.67168.176.0130.016 Error 8223.7327.97 Total 14953.33

9. Slide 12- 9 Copyright © 2010, 2007, 2004 Pearson Education, Inc. All Rights Reserved. The following Minitab display results from a study in which three different teachers taught calculus classes of five different sizes. The class average was recorded for each class. Assuming no effect from interaction between teacher and class size, test the claim that the teacher has no effect on the class average. A.Reject the null hypothesis that the teacher has no effect on class size. B.Fail to reject the null hypothesis that the teacher has no effect on class size. SourceDFSSMSF P Teacher 256.9328.471.0180.404 Class Size 4672.67168.176.0130.016 Error 8223.7327.97 Total 14953.33