Question

No. 4

Sprint int . 8:01 PM С 46% An experiment to compare the spreading rates of five different brands of yellow interior latex paint available in a particular area used 4 gallons (4) of each paint. The sample average spreading rates (ft2/gal) for the five brands were x1,-462.0, x2. -502.8, X3. 427.5, x4.-469.3, and xs.-532.1. The computed value of F was found to be significant at level a 0.05. With MSE 410.8, use Tukey's procedure to investigate significant differences between brands. (Round your answer to two decimal places.) Which means differ significantly from one another? (Select all that apply.) O x1, and x2. X1. and X3. O X1 and X4 X1' and x5. C X2, and X3. 0-2, and-4. X2, and X5 x3, and X4. O x3, and xs. x4, and x5. . O There are no significant differences. You may need to use the appropriate table in the Appendix of Tables to answer this question. Show My Work (optiona) o Consider the following summary data on the modulus of elasticity (x 106 psi) for lumber of three different grades. Grade 163 29 2 7156 0.23 3 7 142 25 Compute a 95% t CI for e«uan *au-n (Round your answers to three decimal places.) x 106 psi

Answer 1

4:

Here we have 5 different paints so k=5

Total number of data values is n = 4*5 = 20

Degree of freedom of error: df = 20 -5 = 15

Critical value for , df=15 and k=5 is

a-0.05

= 4.37

So Tukey's HSD will be

$HSD=q\sqrt{\frac{MSE}{2}\left ( \frac{1}{n_{i}}+\frac{1}{n_{j}} \right )}=4.37\sqrt{\frac{410.8}{2}\left ( \frac{1}{4}+\frac{1}{4} \right )}=44.29$

Following table shows the absolute difference between all possible pairs of mean:

Samples		Samples mean		Absolute Difference
1	2	462	502.8	40.8
1	3	462	427.5	34.5
1	4	462	469.3	7.3
1	5	462	532.1	70.1
2	3	502.8	427.5	75.3
2	4	502.8	469.3	33.5
2	5	502.8	532.1	29.3
3	4	427.5	469.3	41.8
3	5	427.5	532.1	104.6
4	5	469.3	532.1	62.8

Following table shows the differences that are greater than Tukey's HSD:

Samples		Samples mean		Absolute Difference
1	5	462	532.1	70.1
2	3	502.8	427.5	75.3
3	5	427.5	532.1	104.6
4	5	469.3	532.1	62.8

Correct options are:

X1 and X5

X2 and X3

X3 and X5

X4 and X5