http://faculty.uccb.ns.ca/~erudiuk/math135/Math136.htm

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1. A psychologist wants to investigate the effect of social background on the time (in minutes) it takes freshmen to solve a puzzle. A random sample of students from different backgrounds was selected, and given the puzzle to solve under the conditions. The following table shows the results for the time it took the students to solve the puzzle.

Inner City	Urban	Suburban	Rural
16.5	10.9	18.6	14.2
5.2	5.2	8.1	24.5
12.1	10.8	6.4	14.8
14.3	8.9	5.2	24.9
14.3	16.1	7.5	5.1
7.5	12.3	12.9	12.3
8.9	6.9	15.1	10.9

1. Use MINITAB to test whether social background has no effect on the time required to solve the puzzle. Test at the 5% significance level using the P-value approach.

H₀:

H₁:

Test Statistic:

Decision Rule:

Conclusion:

2. Does the confidence intervals support your claim in part (a). Discuss.

 

 

3. Use the Anderson-Darling test to determine whether the normality assumption holds for the Inner City social classification.

H₀:

H₁:

Test Statistic:

Decision Rule:  

Conclusion:

4. Repeat the Anderson-Darling test for the remaining social classes. Based on the plots, discuss whether the normality assumption holds for these classes. Discuss.

H₀:

H₁:

Test Statistic:

Decision Rule:

 

Conclusion:

H₀:

H₁:

Test Statistic:

Decision Rule:

 

Conclusion:

H₀:

H₁:

Test Statistic:

Decision Rule:

 

Conclusion:

 

 

 

 

5. Establish whether the assumption of equal variances for the data sets is reasonable. Test at the 5% significance level and write up an appropriate hypothesis test.

2. In the Journal of Nutrition (July 1995), researchers at the University of Georgia studied the impact of vitamin-B supplement on the kidney. The experimental units were 28 Zuker rats, a species that tend to develop kidney problems. 50% of the rats were classified as obese and the other 50% as lean. Within each group, half were randomly assigned to receive a vitamin-B supplement and the other half was given a regular diet free of vitamin-B. One of the response variables that were measured was the weight in grams of rat’s kidney at the end of a 20-week feeding period. The data is summarized in the following table.
DIET

Rat Size	Regular	Vitamin-B Supplement
Lean	1.68	1.51
	1.80	1.65
	1.71	1.45
	1.81	1.44
	1.47	1.63
	1.37	1.35
	1.71	1.66
Obese	2.35	2.93
	2.97	2.72
	2.54	2.99
	2.93	2.19
	2.84	2.63
	2.05	2.61
	2.82	2.64

1. Would you consider this as a two-factor ANOVA? Discuss.
2. Test at the 5% significance level to determine whether there is a main effect due to the size of the rats. Use the P-value approach.

H₀:

H₁:

Test Statistic:

Decision Rule:

Conclusion:

 

3. Test at the 5% significance level to determine whether there is a main effect due to the diet that was administered. Use the P-value approach.

H₀:

H₁:

Test Statistic:

Decision Rule:

Conclusion:

4. Test at the 5% significance level to determine whether there is an interaction effect between the size of the rats and the diet administered. Use the P-value approach.

H₀:

H₁:

Test Statistic:

Decision Rule:

Conclusion:

5. Use the Anderson-Darling test to determine whether the normality assumption for the two factors was violated. Use the 5% level of significance. Based on the plots and the P-values for the test, is it reasonable to assume that the populations are approximately normally distributed? Discuss.

6. Determine whether the assumption of equal variance for the two-factor experiment is valid. Based on the confidence interval plots for Bartlett’s and Levene’s test , is it reasonable to assume that the variances are equal? Discuss.