Question

In: Statistics and Probability

You may need to use the appropriate technology to answer this question. The following data are...

You may need to use the appropriate technology to answer this question.

The following data are from a completely randomized design.

Treatment
A B C
161 143 126
143 157 121
164 125 137
144 141 139
149 137 151
169 143 124
Sample
mean
155 141 133
Sample
variance
122.8 107.2 130.0

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

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 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.    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.

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