The following are three observations collected from treatment 1, five observatio
ID: 3332995 • Letter: T
Question
The following are three observations collected from treatment 1, five observations collected from treatment 2, and four observations collected from treatment 3. Test the hypothesis that the treatment means are equal at the 0.05 significance level.
Treatment 1
Treatment 2
Treatment 3
8
3
3
11
2
4
10
1
5
3
4
1. (a-1). State the null hypothesis and the alternate hypothesis.
Null hypothesis
H0: 1 = 2
H0: 1 = 2 = 3
1. (a-2). Alternate hypothesis.
H1: Treatment means are all the same
H1: Treatment means are not all the same
b. What is the decision rule? (Round your answer to 2 decimal places.)
c. Compute SST, SSE, and SS total. (Round your answers to 2 decimal places.)
Source
SS
df
MS
F
Treatments
Error
Total
d. Complete an ANOVA table. (Round F, SS to 2 decimal places and MS to 3 decimal places.)
e. State your decision regarding the null hypothesis.
Reject H0.
Do not reject H0.
f. If H0 is rejected, can we conclude that treatment 1 and treatment 2 differ? Use the 95 percent level of confidence.
b)
The following data are given for a two-factor ANOVA with two treatments and three blocks.
Treatment
Block
1
2
A
48
36
B
36
22
C
45
37
Using the 0.05 significance level conduct a test of hypothesis to determine whether the block or the treatment means differ.
a. State the null and alternate hypotheses for treatments.
H0
H1
b. State the decision rule for treatments. (Round your answer to 1 decimal place.)
_________h0 if the statistic is greater than
c. State the null and alternate hypotheses for blocks. (Round your answer to 1 decimal place.)
H0-
H1
Also, state the decision rule for blocks.
___H0 IF the test statistic is greater than _________
d & e. Compute SST, SSB, SS total, and SSE and complete an ANOVA table. (Round your SS, MS values to 3 decimal places and Fvalue to 2 decimal places.)
Source
SS
df
MS
F
Treatments
Blocks
Error
Total
f. Give your decision regarding the two sets of hypotheses.
Decision: Treatments.
H0
Decision: Blocks.
H0
Treatment 1
Treatment 2
Treatment 3
8
3
3
11
2
4
10
1
5
3
4
Explanation / Answer
(a1) H0: 1 = 2 = 3
(a2)H1: Treatment means are not all the same
b. What is the decision rule?
F>4.46
(c)
SST=99.49, SSE=9.42, and SS total=108.91
e. State your decision regarding the null hypothesis.
Reject H0.
(f)critical difference=sqrt(2*mse/r)*t(0.05,error df)=sqrt(2*1.177/3)*2.13=1.89
difference of treatment 1 and treatment 2=9.67-2.25=7.43 is more than critical differnece, so they differ.
a. State the null and alternate hypotheses for treatments.
H0: 1 = 2
H1:: 1 is not = 2
b. State the decision rule for treatments. (Round your answer to 1 decimal place.)
_________h0 if the statistic is greater than 18.51
c. State the null and alternate hypotheses for blocks. (Round your answer to 1 decimal place.)
H0- Block1=Block2=Block3
H1: block are different
Also, state the decision rule for blocks.
___H0 IF the test statistic is greater than 19
f. Give your decision regarding the two sets of hypotheses.
Decision: Treatments.
reject H0
Decision: Blocks.
reject H0
ANOVA Source of Variation SS df MS F P-value F crit Treatements 99.49242 2 49.74621 42.26227 5.59E-05 4.45897 error 9.416667 8 1.177083 Total 108.9091 10Related Questions
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