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  3. the following data are given for a two-factor anov

The following data are given for a two-factor ANOVA with two treatments and three blocks. Block 1...

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Statistics

The following data are given for a two-factor ANOVA with twotreatments and three blocks.

Block 1 2

A 47 30

B 31 29

C 47 36

Using the 0.05 significance level conduct a test of hypothesisto determine whether the block or the treatment means differ.


State the decision rule for treatments. (Round your answerto 1 decimal place.)

State the null and alternate hypotheses for blocks.(Round your answer to 1 decimal place.)

Also, state the decision rule for blocks.

Compute SST, SSB, SS total, and SSE and complete an ANOVA table.(Round your SS, MS values to 3 decimal places andF value to 2 decimal places.)

Answer & Explanation Solved by verified expert
3.8 Ratings (499 Votes)

using excel>data> data analysis> Two way ANOVA

we have

Anova: Two-Factor Without Replication
SUMMARY Count Sum Average Variance
A 2 77 38.5 144.5
B 2 60 30 2
C 2 83 41.5 60.5
1 3 125 41.66667 85.33333
2 3 95 31.66667 14.33333
ANOVA
Source of Variation SS df MS F P-value F crit
treatment 142.3333 2 71.16667 2.497076 0.285953 19
Block 150 1 150 5.263158 0.148743 18.51282
Error 57 2 28.5
Total 349.3333 5

the decision rule for treatment: we will reject HO if F >19.0

the null and alternate hypotheses for blocks is

Ho:all the means of block are same.

Ha : at least two mean differs significantly

the decision rule for blocks : reject Ho if F> 18.5

SST = 142.333, SSB =150 , SS total =349.33, and SSE = 57

an ANOVA table.

ANOVA
Source of Variation SS df MS F P-value
treatment 142.333 2 71.167 2.50 0.285953
Block 150 1 150 5.26 0.148743
Error 57 2 28.5
Total 349.333 5

since p-value for treatment and blocks are greater than so we conclude that means are same for block and treatments
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