Question

The following data are from a completely randomized design. A 164, 142, 169, 145, 149, 167 Sample mean 156 Sample variance 144. B 147, 156,127, 147, 131, 144 Sample mean 142 Sample variance 119.2 C 124, 121, 134, 141, 158, 126, sample mean 134 sample variance 191.6. (1) Compute the sum of squares between treatments. (2) Compute the mean square between treatments. (3) Compute the sum of squares due to error. (4) Compute the mean square due to error (to 1 decimal). (5) Set up the ANOVA table for this problem. Round all Sum of Squares to nearest whole numbers. Round all Mean Squares to one decimal place. Round F to two decimal places. Round your p-value to 4 decimal places. For treatments find the sum of squares, degrees of freedom, mean square, F, and p-value. Do the same for the errors. At a=.05 level of significance test whether the means for the three treatments are equal. Calculate the test statistic to 2 decimals. the p-value?

Answer 1

applying one way ANOVA on given data

1) sum of squares between treatments =1488

2) mean square between treatments =744

3) sum of squares due to error =2274

4) mean square due to error =151.6

5)

Source of Variation	SS	df	MS	F	P-value
Between Groups	1488	2	744	4.91	0.0229
Within Groups	2274	15	151.6
Total	3762	17

from above test statistic =4.91

p value =0.0229

reject null hypothesis