Exercise 1301 The following data are from a completely rando

{Exercise 13.01}

The following data are from a completely randomized design.

Compute the sum of squares between treatments.
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Compute the mean square between treatments.
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Compute the sum of squares due to error.
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Compute the mean square due to error (to 1 decimal).
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Set up the ANOVA table for this problem. Round all Sum of Squares to nearest whole numbers. Round all Mean Squares to one decimal places. Round F to two decimal places.

At the = .05 level of significance, test whether the means for the three treatments are equal.

Calculate the value of the test statistic (to 2 decimals).
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The p-value is _________________

What is your conclusion?
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Solution

From Excel

a) sum of squares between treatments is 1924

b) mean square between treatments is 1924/2 =962

C) sum of squares due to error is 2816

d) mean square due to error is 2816/15 =187.7

Set up the ANOVA table for this problem.

Null hypothesis: the means for the three treatments are equal.

Alternative hypothesis:  the means for the three treatments are not equal.

Test statistic: F cal=5.12

Conclusion :

p value=0.02 and alpha=0.05

Now p value < alpha , we reject the null hypothesis.