Slide 12- 1Copyright © 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

Slide 12- 2Copyright © 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

Source DF SS MS F PFactor 3 13.500 4.500 5.17 0.011Error 16 13.925 0.870Total 19 27.425

Slide 12- 3Copyright © 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

Source DF SS MS F PFactor 3 13.500 4.500 5.17 0.011Error 16 13.925 0.870Total 19 27.425

Slide 12- 4Copyright © 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.

Source DF SS MS F PFactor 3 13.500 4.500 5.17 0.011Error 16 13.925 0.870Total 19 27.425

Slide 12- 5Copyright © 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.

Source DF SS MS F PFactor 3 13.500 4.500 5.17 0.011Error 16 13.925 0.870Total 19 27.425

Slide 12- 6Copyright © 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.

Source DF SS MS F PA 2 415.87305 207.93652 1.88259 .1637B 3 2997.47186 999.15729 9.04603 .0001Interaction 6 707.26626 117.87771 1.06723 .3958Error 46 5080.81667 110.45254Total 57 9201.42784

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.

Slide 12- 7Copyright © 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.

Source DF SS MS F PA 2 415.87305 207.93652 1.88259 .1637B 3 2997.47186 999.15729 9.04603 .0001Interaction 6 707.26626 117.87771 1.06723 .3958Error 46 5080.81667 110.45254Total 57 9201.42784

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.

Slide 12- 8Copyright © 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.

Source DF SS MS F PTeacher 2 56.93 28.47 1.018 0.404Class Size 4 672.67 168.17 6.013 0.016Error 8 223.73 27.97Total 14 953.33

Slide 12- 9Copyright © 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.

Source DF SS MS F PTeacher 2 56.93 28.47 1.018 0.404Class Size 4 672.67 168.17 6.013 0.016Error 8 223.73 27.97Total 14 953.33