One Way ANOVA



|One Way ANOVA |

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|NAME: _______________________________________ |

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Chapter 12

Comparing Many Treatments

1. Analysis of Variance gets its name from the fact that it is a statistical technique for assessing whether the variances of several groups or populations are equal.

(a) True

(b) False

2. One assumption for ANOVA is that the sample variances for each group must be the same.

(a) True

(b) False

3. Fill in the blank. One assumption for ANOVA is that the distribution of the populations from which the samples come is the distribution.

(a) t

(b) F

(c) normal

(d) uniform

4. Fill in the blank. If all the assumptions for ANOVA hold, the test-statistic calculated in ANOVA will follow the distribution.

(a) t

(b) F

(c) normal

(d) uniform

5. Fill in the blank. The null hypothesis for ANOVA states that all I means are equal to each other. The alternative hypothesis states that .

(a) all I means are different from each other

(b) none of the I means are equal to each other

(c) not all I means are equal to each other

(d)

6. Fill in the blank. The basic concept underlying ANOVA is comparing the variation between the sample means (MSB) with the random variation of the observations within the samples (MSW). To have more support for the conclusion that the population means are different, the MSB should be as compared to the MSW.

(a) large

(b) small

7. Fill in the blank. An ANOVA will be used to test if the average rental costs for 1-bedroom apartments for 4 cities are equal. A random sample of 16 1-bedroom apartments from each city will be selected. Respectively, the degrees of freedom for the numerator and denominator of the F-statistic are _____________.

(a) 4 and 16

(b) 4 and 64

(c) 3 and 16

(d) 3 and 60

(e) none of the above answers is correct

Questions 8 through 12 are based on the following ANOVA table.

[pic]

8. Fill in the blank. The number of populations being compared is _______ .

(a) 1

(b) 2

(c) 3

(d) 4

(e) none of the above answers is correct

9. Fill in the blank. The total number of observations, n, is _______ .

(a) 16

(b) 18

(c) 19

(d) 30

(e) none of the above answers is correct

10. Fill in the blank. The mean square between groups, MSB, is _______ .

(a) 90

(b) 30

(c) 180

(d) 480

(e) none of the above answers is correct

11. Fill in the blank. The observed F-test statistic value is _______ .

(a) 2

(b) 3

(c) 30

(d) 16

(e) none of the above answers is correct

12. Fill in the blank. The p-value for the test of equality of the means is _______ .

(a) 0.0783

(b) 0.1565

(c) 0.10

(d) less than 0.05

Questions 13 through 15 are based on the following scenario.

A clinical psychologist wished to compare three methods for reducing hostility levels in university students. A certain test (HLT) was used to measure the degree of hostility. A high score on the test indicated great hostility. Eleven students obtaining high and nearly equal scores were used in the experiment. Four were selected at random from among the 11 problem cases and treated with method 1. Four of the remaining 7 were selected at random and treated with method 2, and the remaining were treated with method 3. All treatments were continued for a one-semester period. Each student was given the HLT test at the end of the semester, with results and output shown below. Assume that the distribution for HLT scores for the three methods are normally distributed with equal population variance.

Test Scores for Method 1: 80 92 87 83

Test Scores for Method 2: 70 81 78 74

Test Scores for Method 3: 63 76 70

[pic]

13. Complete the ANOVA output.

14. Give the appropriate hypotheses for assessing if there is a difference among the mean scores for the three methods.

15. State your conclusions regarding the differences between methods based on the using an overall significance level of 5%.

Questions 16 through 18 are based on the following scenario.

In July, 1995, the magazine "Car and Driver" conducted speed tests of five supercars from five different countries: 1 = Japan (Acura NSX-T), 2= Italy (Ferrari F355), 3 = UK (Lotus Esprit S4S), 4 = Germany (Porsche 911 Turbo), 5 = USA (Dodge Viper RT/10). Car and Driver recorded the top speeds (mph) achieved by these cars using as much distance as necessary. Six measurements were made on each car, three in each direction to cancel any grade or wind factors at the test facility. The analysis of variance results for comparing these speed measurements is provided below.

- - - - - O N E W A Y - - - - -

Variable MPH

By Variable CAR car type

Analysis of Variance

Sum of Mean F F

Source D.F. Squares Squares Ratio Prob.

Between Groups 4 1455.1847 363.7962 25.0849 .0000

Within Groups 25 362.5650 14.5026

Total 29 1817.7497

16. What null and alternative hypotheses are being tested by the F-Ratio in the Analysis of Variance table shown above?

17. What assumptions are required for the F-test in the Analysis of Variance table to be valid?

18. Find The F-ratio and p-value. At a 5% significance level, what is your decision?

(a) Fail to Reject [pic]

(b) Reject [pic]

Questions 48 through 53 are based on the following scenario.

The Silver Family is going to have an addition built to their house. They need to decide which contractor is going to oversee the project. They searched for somebody in the following 3 categories: general contractors, carpenters, and handymen. They visited some people from each category and obtained bids from each one of them. The bids (in thousand dollars) is shown below.

General contractors: 51 47 48 39

Carpenters: 43 36 38 42 33

Handymen: 34 27 39

[pic]

Complete the table .

19. Give the appropriate hypotheses for assessing if there is a difference among the mean bids for the three categories.

20. Test the hypotheses of question 19. Report the value of the observed test statistic, the p-value, and your decision using a 1% significance level.

21. State your conclusions regarding the differences between categories.

Questions 22 through 26 are based on the following scenario.

Three neighbors are having a dispute over whose dog runs the fastest. They decide to do a little experiment. Each dog will run a short distance three times and their times will be recorded. Neighbor Warner knows a little about statistics and decides to use an ANOVA test. The times (in seconds) for the three dogs are listed below.

|Jake = 1 |11.0 |12.9 |12.1 |

|Rover=2 |13.5 |10.8 |14.1 |

|Molly=3 |9.9 |9.8 |9.5 |

22. Besides assuming that the running times of the dogs are normally distributed and that the runs are independent, what else should Neighbor Warner assume?

23. Calculate the MSB. What does this represent?

24. The MSW turns out to be 2.60. What is the value of the test statistic?

25. Based on the test statistic from question 21, what would you tell the 3 neighbors?

26. Determine which Runner(s) differ? Jake & Rover

Jake & Molly

Rover &Molly

They are all differernt from each others

|Multiple Comparisons |

|Tukey | |

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