#9 These are the WEIGHTS of three groups (call these \"conditions\") of men from

Question

#9 These are the WEIGHTS of three groups (call these "conditions") of men from three different States. Do a One-Way ANOVA test to determine the statistics below: Group 1 216 198 240 187 176 Group 2 202 213 284 Group 3 170 165 182 197 201 210 FILL IN THE TABLE BELOW WITH THESE VALUES: (a) Sum of Squares factor (b) Sum of Squares Error (c) df for the Numerator (d) df for the Denominator (e) Mean Square Factor (f) Mean square Error (g) The F-test statistic (h) The F-critical value (assume alpha : 596) CITE HERE: (i) the P-value (software OK) i) Accept or Reject Ho? (if test/critical F statistic conclusion differs from P-value conclusion, something is wrong.) AND EXPLAIN WHAT THIS MEANS MS df SSQ(B&E;) df SSQ CONDITION (e(g) SOURCE ERROR TOTAL (h) is the critical F-value from a Table of your choice. See if you can figure it out.

Explanation / Answer

Step 1

Null Hypothesis Ho : µ1 =µ2 =µ3

Alternative Hypothesis :µ1 µ2 µ3

Step 2

Degrees of freedom between = k - 1 = 3 - 1 = 2

Degrees of freedom Within = n - k = 15 - 3 = 12

Degrees of freedom Total F( k-1,n - k,) at 0.05 is = F Crit = 3.885

Step 3

Grand Mean = G / N = 203.4+227.4+183 / 3 = 204.6

SST = ( Xi - GrandMean)^2 = (216-204.6)^2 + (198-204.6)^2 + (240-204.6)^2 + ……..& so on = 12859.6

SS Within = (Xi - Mean of Xi ) ^2 =,(216-203.4)^2 + (198-203.4)^2 + (240-203.4)^2 + ……..& so on = 7920.4

SS Between = SST - SS Within = 12859.6 - 7920.4 = 4939.2

Step 4

Mean Square Between = SS Between / df Between = 4939.2/2 = 2469.6

Mean Square Within = SS Within / df Within = 7920.4/12 = 660.033

Step 5

F Cal = MS Between / Ms Within = 2469.6/660.033 = 3.742

We got |F cal| = 3.742 & |F Crit| =3.885

MAKE DECISION

Hence Value of |F cal| < |F Crit|and Here We Accept Ho

Treatments ONE WAY ANOVA Mean = X /n Group1 216 198 240 187 176 203.4 Group2 202 213 284 228 210 227.4 Group3 170 165 182 197 201 183

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