Question

Suppose samples of six different brands of diet or imitation margarine were analyzed to determine the level of physiologically active polyunsaturated fatty acids (PAPUFA, in percent), resulting in the data shown in the accompanying table. Imperial 14.1 13.6 14.4 14.3 Parkay 12.8 12.5 13.5 13.0 12.3 Blue Bonnet 13.5 13.4 14.1 14.3 Chiffon 13.2 12.7 12.6 14.1 Mazola 16.8 17.3 16.4 17.3 18.0 Fleischmann's 18.1 17.2 18.7 18.4 (a) Test for differences among the true average PAPUFA percentages for the different brands. Use α = 0.05. Calculate the test statistic. (Round your answer to two decimal places.) F = Correct: Your answer is correct. What can be said about the P-value for this test? P-value > 0.100 0.050 < P-value < 0.100 0.010 < P-value < 0.050 0.001 < P-value < 0.010 P-value < 0.001 Correct: Your answer is correct. What can you conclude? Reject H0. There is not convincing evidence that the mean PAPUFA percentages for the six brands are not all equal. Reject H0. There is convincing evidence that the mean PAPUFA percentages for the six brands are not all equal. Fail to reject H0. There is not convincing evidence that the mean PAPUFA percentages for the six brands are not all equal. Fail to reject H0. There is convincing evidence that the mean PAPUFA percentages for the six brands are not all equal. Correct: Your answer is correct. (b) Use the T-K procedure to compute 95% simultaneous confidence intervals for all differences between means. (Round your answers to three decimal places.) Imperial and Parkay Incorrect: Your answer is incorrect. , Incorrect: Your answer is incorrect. Imperial and Blue Bonnet , Imperial and Chiffon , Imperial and Mazola , Imperial and Fleischmann's , Parkay and Blue Bonnet , Parkay and Chiffon , Parkay and Mazola , Parkay and Fleischmann's , Blue Bonnet and Chiffon , Blue Bonnet and Mazola , Blue Bonnet and Fleischmann's , Chiffon and Mazola , Chiffon and Fleischmann's , Mazola and Fleischmann's ,

Answer 1

Suppose samples of six different brands of diet or imitation margarine were analyzed to determine the level of physiologically active polyunsaturated fatty acids (PAPUFA, in percent), resulting in the data shown in the accompanying table.

Imperial 14.1 13.6 14.4 14.3

Parkay 12.8 12.5 13.5 13.0 12.3

Blue Bonnet 13.5 13.4 14.1 14.3

Chiffon 13.2 12.7 12.6 14.1

Mazola 16.8 17.3 16.4 17.3 18.0

Fleischmann's 18.1 17.2 18.7 18.4

1. Test for differences among the true average PAPUFA percentages for the different brands. Use α = 0.05. Calculate the test statistic. (Round your answer to two decimal places.)

F = 72.20

What can be said about the P-value for this test?

P-value < 0.001

What can you conclude?

Reject H0. There is convincing evidence that the mean PAPUFA percentages for the six brands are not all equal.

1. Use the T-K procedure to compute 95% simultaneous confidence intervals for all differences between means. (Round your answers to three decimal places.)

Difference of Levels	Difference of Means	SE of Difference	95% CI	T-Value	Adjusted P-Value
Parkay - Imperial	-1.280	0.366	(-2.432, -0.128)	-3.50	0.024
BlueBonnet - Imperial	-0.275	0.386	(-1.489, 0.939)	-0.71	0.978
Chiffon - Imperial	-0.950	0.386	(-2.164, 0.264)	-2.46	0.183
Mazola - Imperial	3.060	0.366	(1.908, 4.212)	8.36	0.000
Fleischmann - Imperial	4.000	0.386	(2.786, 5.214)	10.36	0.000
BlueBonnet - Parkay	1.005	0.366	(-0.147, 2.157)	2.75	0.110
Chiffon - Parkay	0.330	0.366	(-0.822, 1.482)	0.90	0.942
Mazola - Parkay	4.340	0.345	(3.254, 5.426)	12.57	0.000
Fleischmann - Parkay	5.280	0.366	(4.128, 6.432)	14.42	0.000
Chiffon - BlueBonnet	-0.675	0.386	(-1.889, 0.539)	-1.75	0.518
Mazola - BlueBonnet	3.335	0.366	(2.183, 4.487)	9.11	0.000
Fleischmann - BlueBonnet	4.275	0.386	(3.061, 5.489)	11.08	0.000
Mazola - Chiffon	4.010	0.366	(2.858, 5.162)	10.95	0.000
Fleischmann - Chiffon	4.950	0.386	(3.736, 6.164)	12.83	0.000
Fleischmann - Mazola	0.940	0.366	(-0.212, 2.092)	2.57	0.152

MINITAB used

One-way ANOVA: Imperial, Parkay, BlueBonnet, Chiffon, ... eischmann

Method

Null hypothesis	All means are equal
Alternative hypothesis	Not all means are equal
Significance level	α = 0.05

Equal variances were assumed for the analysis.

Factor Information

Factor	Levels	Values
Factor	6	Imperial, Parkay, BlueBonnet, Chiffon, Mazola, Fleischmann

Analysis of Variance

Source	DF	Adj SS	Adj MS	F-Value	P-Value
Factor	5	107.538	21.5076	72.20	0.000
Error	20	5.957	0.2979
Total	25	113.495

Model Summary

S	R-sq	R-sq(adj)	R-sq(pred)
0.545779	94.75%	93.44%	91.11%

Means

Factor	N	Mean	StDev	95% CI
Imperial	4	14.100	0.356	(13.531, 14.669)
Parkay	5	12.820	0.466	(12.311, 13.329)
BlueBonnet	4	13.825	0.443	(13.256, 14.394)
Chiffon	4	13.150	0.686	(12.581, 13.719)
Mazola	5	17.160	0.602	(16.651, 17.669)
Fleischmann	4	18.100	0.648	(17.531, 18.669)

Pooled StDev = 0.545779

Tukey Pairwise Comparisons

Grouping Information Using the Tukey Method and 95% Confidence

Factor	N	Mean	Grouping
Fleischmann	4	18.100	A
Mazola	5	17.160	A
Imperial	4	14.100		B
BlueBonnet	4	13.825		B	C
Chiffon	4	13.150		B	C
Parkay	5	12.820			C

Means that do not share a letter are significantly different.

Tukey Simultaneous Tests for Differences of Means

Difference of Levels	Difference of Means	SE of Difference	95% CI	T-Value	Adjusted P-Value
Parkay - Imperial	-1.280	0.366	(-2.432, -0.128)	-3.50	0.024
BlueBonnet - Imperial	-0.275	0.386	(-1.489, 0.939)	-0.71	0.978
Chiffon - Imperial	-0.950	0.386	(-2.164, 0.264)	-2.46	0.183
Mazola - Imperial	3.060	0.366	(1.908, 4.212)	8.36	0.000
Fleischmann - Imperial	4.000	0.386	(2.786, 5.214)	10.36	0.000
BlueBonnet - Parkay	1.005	0.366	(-0.147, 2.157)	2.75	0.110
Chiffon - Parkay	0.330	0.366	(-0.822, 1.482)	0.90	0.942
Mazola - Parkay	4.340	0.345	(3.254, 5.426)	12.57	0.000
Fleischmann - Parkay	5.280	0.366	(4.128, 6.432)	14.42	0.000
Chiffon - BlueBonnet	-0.675	0.386	(-1.889, 0.539)	-1.75	0.518
Mazola - BlueBonnet	3.335	0.366	(2.183, 4.487)	9.11	0.000
Fleischmann - BlueBonnet	4.275	0.386	(3.061, 5.489)	11.08	0.000
Mazola - Chiffon	4.010	0.366	(2.858, 5.162)	10.95	0.000
Fleischmann - Chiffon	4.950	0.386	(3.736, 6.164)	12.83	0.000
Fleischmann - Mazola	0.940	0.366	(-0.212, 2.092)	2.57	0.152

Individual confidence level = 99.49%