The data that follow are observations collected from an experiment that compared
ID: 3182700 • Letter: T
Question
The data that follow are observations collected from an experiment that compared four treatments, A, B, C, and D, within each of three blocks, using a randomized block design.
a. Do the data present sufficient evidence to indicate differences among the treatment means? Test using alpha = 0.05.
b. Do the data present sufficient evidence to indicate differences among the block means? Test using alpha = 0.05.
c.Find a 95% confidence interval for the difference in means for treatments A and B.
Block A B C D Total 1 6 10 8 9 33 2 4 9 5 7 25 3 12 15 14 14 55 Total 22 34 30 30 113Explanation / Answer
Answer:
a. Do the data present sufficient evidence to indicate differences among the treatment means? Test using alpha = 0.05.
Calculated Test value F=19.19, P=0.002 which is < 0.05 level. Ho is rejected.
There is sufficient evidence to indicate differences among the treatment means.
b. Do the data present sufficient evidence to indicate differences among the block means? Test using alpha = 0.05.
Calculated Test value F=135.75, P=0.000 which is < 0.05 level. Ho is rejected.
There is sufficient evidence to indicate differences among the block means.
c.Find a 95% confidence interval for the difference in means for treatments A and B.
95% CI for difference in means for treatments A and B= ( -5.886, -2.114)
General Linear Model: data versus Block, Treatment
Method
Factor coding (-1, 0, +1)
Factor Information
Factor Type Levels Values
Block Fixed 3 1, 2, 3
Treatment Fixed 4 A, B, C, D
Analysis of Variance
Source DF Adj SS Adj MS F-Value P-Value
Block 2 120.667 60.3333 135.75 0.000
Treatment 3 25.583 8.5278 19.19 0.002
Error 6 2.667 0.4444
Total 11 148.917
Model Summary
S R-sq R-sq(adj) R-sq(pred)
0.666667 98.21% 96.72% 92.84%
Tukey Simultaneous Tests for Differences of Means
Difference
of Treatment Difference SE of Simultaneous Adjusted
Levels of Means Difference 95% CI T-Value P-Value
B - A 4.000 0.544 ( 2.114, 5.886) 7.35 0.001
C - A 1.667 0.544 (-0.219, 3.553) 3.06 0.080
D - A 2.667 0.544 ( 0.781, 4.553) 4.90 0.011
C - B -2.333 0.544 (-4.219, -0.447) -4.29 0.020
D - B -1.333 0.544 (-3.219, 0.553) -2.45 0.167
D - C 1.000 0.544 (-0.886, 2.886) 1.84 0.343
Individual confidence level = 98.66%
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