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Business Statistics in Practice Study Set 1
Quiz 10: Experimental Design and Analysis of Variance
Path 4
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Question 81
Essay
 BlockÂ
1
2
3
4
5
 Tr1Â
2
1
2
3
2
 Tr2Â
4
4
1
1
2.5
 TR3Â
3
4
3
2
3
 MeanÂ
2
3
3
2
 overall meanÂ
=
2.5
\begin{array} { l l l l l l } \text { Block } & 1 & 2 & 3 & 4 & 5 \\\text { Tr1 } & 2 & 1 & 2 & 3 & 2 \\\text { Tr2 } & 4 & 4 & 1 & 1 & 2.5 \\\text { TR3 } & 3 & 4 & 3 & 2 & 3 \\\text { Mean } & 2 & 3 & 3 & 2 & \text { overall mean } = 2.5\end{array}
 BlockÂ
 Tr1Â
 Tr2Â
 TR3Â
 MeanÂ
​
1
2
4
3
2
​
2
1
4
4
3
​
3
2
1
3
3
​
4
3
1
2
2
​
5
2
2.5
3
 overall meanÂ
=
2.5
​
Consider the randomized block design with 4 blocks and 3 treatments (groups) given above -What is the blocks mean square?
Question 82
Essay
Find Tukey's simultaneous 95 percent confidence interval for
μ
1
−
μ
2
\mu _ { 1 } - \mu _ { 2 }
μ
1
​
−
μ
2
​
where
x
ˉ
1
\bar { x } _ { 1 }
x
ˉ
1
​
= 51.5,
x
ˉ
2
\bar { x } _ { 2 }
x
ˉ
2
​
= 55.8,and MSE = 6.125.There were 4 treatments and 24 observations in total and the number of observations were equal in each group.
Question 83
Essay
Find an individual 95 percent confidence interval for
μ
1
−
μ
2
\mu _ { 1 } - \mu _ { 2 }
μ
1
​
−
μ
2
​
where
x
ˉ
1
\bar { x } _ { 1 }
x
ˉ
1
​
= 33.98,
x
ˉ
2
\bar { x } _ { 2 }
x
ˉ
2
​
= 36.56,and MSE = 0.669.There were 15 observations in total and 3 treatments.Assume that the number of observations in each treatment is equal.
Question 84
Essay
 BlockÂ
1
2
3
4
5
 Tr1Â
2
1
2
3
2
 Tr2Â
4
4
1
1
2.5
 TR3Â
3
4
3
2
3
 MeanÂ
2
3
3
2
 overall meanÂ
=
2.5
\begin{array} { l l l l l l } \text { Block } & 1 & 2 & 3 & 4 & 5 \\\text { Tr1 } & 2 & 1 & 2 & 3 & 2 \\\text { Tr2 } & 4 & 4 & 1 & 1 & 2.5 \\\text { TR3 } & 3 & 4 & 3 & 2 & 3 \\\text { Mean } & 2 & 3 & 3 & 2 & \text { overall mean } = 2.5\end{array}
 BlockÂ
 Tr1Â
 Tr2Â
 TR3Â
 MeanÂ
​
1
2
4
3
2
​
2
1
4
4
3
​
3
2
1
3
3
​
4
3
1
2
2
​
5
2
2.5
3
 overall meanÂ
=
2.5
​
Consider the randomized block design with 4 blocks and 3 treatments (groups) given above -What is the between-groups mean square?
Question 85
Essay
Consider the following one-way ANOVA table.
 SourceÂ
 d.f.Â
 Sum of SquaresÂ
 ModelÂ
3
213.88125
 ErrorÂ
20
11.208333
 TotalÂ
23
225.0895
\begin{array} { l c c } \text { Source } & \text { d.f. } & \text { Sum of Squares } \\\text { Model } & 3 & 213.88125 \\\text { Error } & 20 & 11.208333 \\\text { Total } & 23 & 225.0895\end{array}
 SourceÂ
 ModelÂ
 ErrorÂ
 TotalÂ
​
 d.f.Â
3
20
23
​
 Sum of SquaresÂ
213.88125
11.208333
225.0895
​
What is the value of the F statistic for testing for a difference between group means?
Question 86
Essay
A completely randomized design with three groups,each with five measurements.The one-way ANOVA yields a between-groups sum of squares treatment of 17.0493 and error sum of squares of 8.028.Compute the F statistic.