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The following data are from a completely randomized design. Treatment 164 149 142 157 167 124 145 149 149 137 169 136 156 142 144 141.6 119.6 126 122 133 141 152 130 134 Sample mean Sample variance a. Compute the sum of squares between treatments. Round the intermediate calculations to whole number 1488 b. Compute the mean squ are between treatments. 744 c. Compute the sum of squares due to error. 135.33 d. Compute the mean square due to error (to 1 decimal). e. Set up the ANOVA table for this problem. Round all Sum of Squares to the nearest whole number. Round all Mean Squares to one decimal place. Round Fto two decimal places. Round p-value to four decimal places. Source of Variation Sum of Squares Degrees of Freedom Mean Square p-value Error Total

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X1 164 142 167 145 149 169 X2 149 157 124 149 137 136 Total 439 421 424 435 438 435 18 2592 grand mean Xgrand144.0000 X3 126 133 141 152 Total-X - 936 156.0000 146736 144.0000 852 142.0000 121692 141.6000 Average-CD</n - 134.0000 108334 119.6000 Total observation 18 number of groups between groups degree of freedom dfbg -k-1- within groups degree of freedom dfw-N-k - Total degree of freedom 15 df 17 156.0000 142.0000 134.0000 144.000 141.600 119.600 720.00 708.00 598.00 1488.0000 2026.0000 864.00 24.00 600.00 total 2nXgand)1488.0000 2026.0000 3514.0000 sum of square between groups SSG- 2(n-1)s2 SSG+SSE- sum of square within groups SSE- total sum of square Summary table Source of variation between within total 1488.000 2026.000 3514.000 df 2.0000 15.0000 17.0000 MS 744.00 135.07 5.51

a)

sum of square between treatments=1488

b)

MS between treatments =744

c)

sum of square due to error =2026

d)

MS due to error =135.1e)

Source of variation SS df MS F p vlaue
treatment 1488.000 2.0000 744.0 5.51 0.0161
error 2026.000 15.0000 135.1
total 3514.000 17.0000
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