{Exercise 13.01} The following data are from a completely randomized design. Com

Question

{Exercise 13.01}

The following data are from a completely randomized design.

Compute the sum of squares between treatments.
______

Compute the mean square between treatments.
______

Compute the sum of squares due to error.
______

Compute the mean square due to error (to 1 decimal).
______

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).
______

The p-value is _________________

What is your conclusion?
_________________

Treatment A B C 163 144 124 142 159 122 168 129 134 145 144 142 148 132 152 188 150 130 Sample mean 159 143 134 Sample variance 308.8 124.8 129.6

Explanation / Answer

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.

Anova: Single Factor SUMMARY Groups Count Sum Average Variance A 6 954 159 308.8 B 6 858 143 124.8 C 6 804 134 129.6 ANOVA Source of Variation SS df MS F P-value F crit Between Groups 1924 2 962 5.12429 0.020133 3.68232 Within Groups 2816 15 187.7333 Total 4740 17

Related Questions

Navigate

• Browse (All)
• Browse #
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.