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The following are six observations collected from treatment 1, four observations collected from treatment 2, and five observationscollected from treatment 3. Test the hypothesis at the 0.05 significance level that the treatment means are equalTreatment 1 Treatment 2 Treatment 3913102091114151314121510a. State the null and the alternate hypothesis.Ho u1р2рзH1 Treatment means are notall the same.b. What is the decision rule? (Round your answer to 2 decimal places.)Reject Ho if F>3.89 b. What is the decision rule? (Round your answer to 2 decimal places.)Reject Ho if F3.89Rectangular Snipc. Compute SST, SSE, and SS total. (Round your answers to 2 decimal places.)70.40 SSESST=SS total =152.93d. Complete the ANOVA table. (Round your SS, MS and Fvalues to 2 decimal places.)SourceSSdfMSFTreatments70.4025.12Error126.88Total152.9314

Question
The following are six observations collected from treatment 1, four observations collected from treatment 2, and five observations
collected from treatment 3. Test the hypothesis at the 0.05 significance level that the treatment means are equal
Treatment 1 Treatment 2 Treatment 3
9
13
10
20
9
11
14
15
13
14
12
15
10
a. State the null and the alternate hypothesis.
Ho u1
р2
рз
H1 Treatment means are not
all the same.
b. What is the decision rule? (Round your answer to 2 decimal places.)
Reject Ho if F>
3.89
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The following are six observations collected from treatment 1, four observations collected from treatment 2, and five observations collected from treatment 3. Test the hypothesis at the 0.05 significance level that the treatment means are equal Treatment 1 Treatment 2 Treatment 3 9 13 10 20 9 11 14 15 13 14 12 15 10 a. State the null and the alternate hypothesis. Ho u1 р2 рз H1 Treatment means are not all the same. b. What is the decision rule? (Round your answer to 2 decimal places.) Reject Ho if F> 3.89

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b. What is the decision rule? (Round your answer to 2 decimal places.)
Reject Ho if F
3.89
Rectangular Snip
c. Compute SST, SSE, and SS total. (Round your answers to 2 decimal places.)
70.40 SSE
SST=
SS total =
152.93
d. Complete the ANOVA table. (Round your SS, MS and Fvalues to 2 decimal places.)
Source
SS
df
MS
F
Treatments
70.40
2
5.12
Error
12
6.88
Total
152.93
14
help_outline

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b. What is the decision rule? (Round your answer to 2 decimal places.) Reject Ho if F 3.89 Rectangular Snip c. Compute SST, SSE, and SS total. (Round your answers to 2 decimal places.) 70.40 SSE SST= SS total = 152.93 d. Complete the ANOVA table. (Round your SS, MS and Fvalues to 2 decimal places.) Source SS df MS F Treatments 70.40 2 5.12 Error 12 6.88 Total 152.93 14

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Step 1

Note:

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Step 2

Explanation:

Part (a):

The test hypotheses are:

Null hypothesis: H0: μ1 = μ2 = μ3; vs.

Alternate hypothesis: H1: Treatment means are not all the same.

Part (b):

The F-test is used for testing the above hypotheses.

Here, number of treatments, k = 3.

Total number of observations, n = 6 + 4 + 5 = 15.

Thus, the numerator degrees of freedom for the F-distribution is, k – 1 = 2; the denominator degrees of freedom, nk = 12.

The significance level is, α = 0.05.

Thus, the critical value is, ; k – 1, nk = F0.05; 2, 12.

Using Excel formula, =F.INV.RT(0.05,2,12), the critical value is 3.89.

The decision rule is: Reject H0 if F > 3.89.

Part (c...

Anova: Single Factor
SUMMARY
Groups
Count
Variance
Sum
Average
Treatment 1
6
58 9.666666667 3.066666667
4
Treatment 2
60
15 11.33333333
Treatment 3
5
63
12.6
8.3
ANOVA
Source of Variation
SS
df
F
P-value
F crit
MS
Between Groups
70.4
35.2 5.117932149 0.024703779 3.885293835
Within Groups
82.53333333
12 6.877777778
Total
152.9333333
14
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Anova: Single Factor SUMMARY Groups Count Variance Sum Average Treatment 1 6 58 9.666666667 3.066666667 4 Treatment 2 60 15 11.33333333 Treatment 3 5 63 12.6 8.3 ANOVA Source of Variation SS df F P-value F crit MS Between Groups 70.4 35.2 5.117932149 0.024703779 3.885293835 Within Groups 82.53333333 12 6.877777778 Total 152.9333333 14

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Hypothesis Testing

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