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	13.4	13.0	12.3
Blue Bonnet	13.5	13.4	14.1	14.4
Chiffon	13.2	12.7	12.6	13.9
Mazola	16.8	17.2	16.4	17.3	18.0
Fleischmann's	18.1	17.2	18.7	18.4

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

(

)

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

Following is the ANOVA:

ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	107.9815	5	21.59629	77.65657	2.11E-12	2.71089
Within Groups	5.562	20	0.2781
Total	113.5435	25

And the sample means are:

Groups	Count	Sum	Average
Imperial	4	56.4	14.1
Parkay	5	64	12.8
Blue Bonnet	4	55.4	13.85
Chiffon	4	52.4	13.1
Mazola	5	85.7	17.14
Fleischmann's	4	72.4	18.1

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Critical value for , df=20 and k=6 is

From table:

MSE = 0.2781

So Tukey's HSD will be calculated as follows

And the required confidence interval are calculated as follows,

For :

Following table shows the required intervals: