Question

Question 1. Samples of peanut butter produced by three different manufacturers are examined for aflatoxin content, and the results are shown in the table. The data are also available in a separate file on Canvas. We will use analysis of variance to test whether the three brands differ in mean aflatoxin content. Nowe 0 inawa Brand A Brand B 3.5 3.3 0.0 7.7 6.2 2.5 3.9 7.8 4.6 5.8 5.5 3.6 3.0 3.4 5.4 0.0 7.3 5.1 3.2 5.6 3.5 3.3 4.8 0.0 4.7 2.6 0.6 6.7 2.7 (a) Verify that the assumption of normality has not been violated. Provide the p-value of each test: for Brand A for Brand B for Brand C 12.5 5.3 1.4 8.8 1.7 6.2 8.8 7.6 3.5 3.8 10.3 5.4 (b) Verify that the assumption of equality of variances has not been violated. Provide the p-value of the appropriate test. (c) Is there evidence to conclude that the means are different for the various brands? (yes or no) Provide the p-value of the test you use to make this decision. (d) Identify which, if any, brands have different means, and provide the p-value of each test. Is the mean for Brand A different than the mean for Brand B(yes or no)? p-value? Is the mean for Brand A different than the mean for Brand C (yes or no)? p-value? Is the mean for Brand B different than the mean for Brand C (yes or no)? p-value?

Answer 1

(a) Brand A = 0.486

Brand B = 0.825

Brand C = 0.881

Probability Plot of Brand A, Brand B, Brand C Normal - 95% CI 99 Variable Brand A Brand B Brand C 95 90 80 Mean StDev N AD P 3.38 2.488 15 0.325 0.486 4.427 1.852 15 0.211 0.825 6.047 3.143 15 0.190 0.881 Percent 70 60 50 40 30 20 10 5 1 -5 10 15 5 Data

(b) The p-value is 0.231.

Method	Test Statistic	P-Value
Multiple comparisons	—	0.166
Levene	1.52	0.231

(c) yes

p-value = 0.022

Source	DF	Adj SS	Adj MS	F-Value	P-Value
Factor	2	54.16	27.078	4.17	0.022
Error	42	272.99	6.500
Total	44	327.15

(d) no, p-value = 0.267

yes, p-value = 0.006

no, p-value = 0.089

Difference of Levels	Difference of Means	SE of Difference	95% CI	T-Value	Adjusted P-Value
Brand B - Brand A	1.047	0.931	(-0.832, 2.925)	1.12	0.267
Brand C - Brand A	2.667	0.931	(0.788, 4.545)	2.86	0.006
Brand C - Brand B	1.620	0.931	(-0.259, 3.499)	1.74	0.089