Question

In: Statistics and Probability

The following data are from a completely randomized design. Treatment A B C 163 141 127...

The following data are from a completely randomized design.

Treatment
A B C
163 141 127
142 156 122
166 125 137
145 142 141
149 137 151
165 145 120
Sample
mean
155 141 133
Sample
variance
118.0 102.8 146.0

(a)

Compute the sum of squares between treatments.

(b)

Compute the mean square between treatments.

(c)

Compute the sum of squares due to error.

(d)

Compute the mean square due to error. (Round your answer to two decimal places.)

(e)

Set up the ANOVA table for this problem. (Round your values for MSE and F to two decimal places, and your p-value to four decimal places.)

Source
of Variation
Sum
of Squares
Degrees
of Freedom
Mean
Square
F p-value
Treatments
Error
Total

(f)

At the α = 0.05 level of significance, test whether the means for the three treatments are equal.

State the null and alternative hypotheses.

H0: At least two of the population means are equal.
Ha: At least two of the population means are different.H0: Not all the population means are equal.
Ha: μA = μB = μC    H0: μAμBμC
Ha: μA = μB = μCH0: μA = μB = μC
Ha: μAμBμCH0: μA = μB = μC
Ha: Not all the population means are equal.

Find the value of the test statistic. (Round your answer to two decimal places.)

Find the p-value. (Round your answer to four decimal places.)

p-value =

State your conclusion.

Do not reject H0. There is not sufficient evidence to conclude that the means for the three treatments are not equal.Reject H0. There is not sufficient evidence to conclude that the means for the three treatments are not equal.    Do not reject H0. There is sufficient evidence to conclude that the means for the three treatments are not equal.Reject H0. There is sufficient evidence to conclude that the means for the three treatments are not equal.

Solutions

Expert Solution

Solution:

We can use the excel ANOVA data analysis tool to find the answer to the given questions. The excel output is given below:

(a) Compute the sum of squares between treatments.

Answer:

(b) Compute the mean square between treatments.

Answer:

(c) Compute the sum of squares due to error.

Answer:

(d) Compute the mean square due to error. (Round your answer to two decimal places.)

Answer:

(e) Set up the ANOVA table for this problem. (Round your values for MSE and F to two decimal places, and your p-value to four decimal places.)

Answer:

(f) At the α = 0.05 level of significance, test whether the means for the three treatments are equal.

State the null and alternative hypotheses.

Answer: H0: μA = μB = μC
Ha: Not all the population means are equal.

Find the value of the test statistic. (Round your answer to two decimal places.)

Answer:

Find the p-value. (Round your answer to four decimal places.)

Answer:

State your conclusion.

Answer: Reject H0. There is sufficient evidence to conclude that the means for the three treatments are not equal.


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