True or False on ANOVA Tests

TRUE OR FALSE?
1. More variation should be expected between larger samples, which is apparent by the chi-square distribution.
2. A test of independence can be used to determine a cause-and-effect link between the variables being studied.
3. Using the F distribution for a one-way ANOVA, the degrees of freedom for the denominator will always exceed the degrees of freedom for the numerator
Sect. 11-2, p. 600
#11. Deaths from Car Crashes. Randomly selected deaths from car crashes were obtained, and the results are included in the table below (based on data from the insurance Institute for Highway Safety). Use a 0.05 significance level to test the claim that car crash fatalities occur with equal frequency on the different days of the week. How might the results be explained? Why does there appear to be an exceptionally large number of car crash fatalities on Saturday?
Day Sun Mon Tues Wed Thurs Fri Sat
Number of Fatalities 132 98 95 98 105 133 158
21. M&M Candies. Mars, Inc. claims that its M&M plain candies are distributed with the following color percentages: 16% green, 20% orange, 14% yellow, 24% blue, 13% red, and 13% brown. Refer to Data Set 13 in Appendix B and use the sample data to test the claim that the color distribution is as claimed by Mars, Inc. Use a 0.05 significance level.
Sect. 11-3, p. 616
#11. Accuracy of Polygraph Tests. The data in the accompanying table summarize results from tests of the accuracy of polygraphs (based on data from the Office of Technology Assessment). Use a 0.05 significance level to test the claim that whether the subject lies is independent of the polygraph indication. What do the results suggest about the effectiveness of polygraphs?
Polygraph Indicated Truth Polygraph Indicated
Dog identified subject as cancerous 22 32
Dog did not identify subject as cancerous 32 282

17. Occupational Hazards. Use the data in the table to test the claim that occupations is independent of whether the cause of death was homicide. The table is based on data from the U.S. Department of Labor, Bureau of Labor Statistics. Does any particular occupation appear to be most prone to homicides? If so, which one?
Police Cashiers Taxi Drivers Guards
Homicide 82 107 70 59
Cause of death other than homicide 92 9 29 42

Sect. 12-2, p. 649

#11. Head Injury in a Car Crash. The head injury data (in hic) are given below. Use a 0.05 significance level to test the null hypothesis that the different weight categories have the same mean. Do the data suggest that larger cars are safer?
Subcompact: 681 428 917 898 420
Compact: 643 655 442 514 525
Midsize: 469 727 525 454 259
Full-size: 384 656 602 687 360

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...000 14.368
819 819.000 0.000 30.017

30.02 chi-square
6 df
3.90E-05 p-value

Conclusion:
Since the p value is less than 0.05 there is no evidence to accept the null. Hence we conclude that car crash fatalities occur with unequal frequency on the different days of the week.

21. M&M Candies. Mars, Inc. claims that its M&M plain candies are distributed with the following color percentages: 16% green, 20% orange, 14% yellow, 24% blue, 13% red, and 13% brown. Refer to Data Set 13 in Appendix B and use the sample data to test the claim that the color distribution is as claimed by Mars, Inc. Use a 0.05 significance level.
Solution:
Null hypothesis:
H0: M&M plain candies with the observed colours is equal to the expected colours.
Alternative hypothesis:
H1: M&M plain candies with the observed colours is equal to the expected colours.

Level of significance:
The level of significance, α = 0.05
Decision rule:
Reject the null hypothesis if p-value < 0.05 otherwise accept the null hypothesis.

Test statistic:

Where o ij is the observed frequencies and the e ij is the expected frequencies

Goodness of Fit Test

observed expected O - E (O - E)² / E
16 16.667 -0.667 0.027
20 16.667 3.333 0.667
14 16.667 -2.667 0.427
24 16.667 7.333 3.227
13 16.667 -3.667 0.807
13 16.667 -3.667 0.807
100 100.000 0.000 5.960

5.96 chi-square
5 df
.3101 p-value

Conclusion:
Since the p value is greater than 0.05 we may to accept the null. Hence we conclude that M&M plain candies with the observed colours is equal to the expected colours.

Sect. 11-3, p. 616
#11. Accuracy of Polygraph Tests. The data in the accompanying table summarize results from tests of the accuracy of polygraphs (based on data from the Office of Technology Assessment). Use a 0.05 significance level to test the claim that whether the subject lies is independent of the polygraph indication. What do the results suggest about the effectiveness of polygraphs?
Polygraph Indicated Truth Polygraph Indicated
Dog identified subject as cancerous 22 32
Dog did not identify subject as cancerous 32 282

Solution:
Null hypothesis:
H0: The subject lies is independent of the polygraph indication
Alternative hypothesis:
H1: The subject lies is dependent of the polygraph ...