A sports researcher was interested in differences in hitting habits among profes

Question

A sports researcher was interested in differences in hitting habits among professionals in difference bolts. Thus, a standard written test of eating habits was adminitered to 12 randomly selected professional sportsmen, four each from soccer, football and basketball. The results are as follows:

X1= 34.5 S12 = 461.67

X2 = 41 S22 = 347.33

X3= 46.75 S32 = 116.25

-What are the numerator and denominator degrees of freedom?

-Compute S 2 M and hence compute S2 Between

-Compute within-group population variance estimate S2 within

-Compute F ratio

-What is your decision? Is there a difference in hitting habits among professional sportsmen in the three sports? (Use the 0.05 significant level).

Soccer Players Football Players Basketball Players 34 27 35 18 28 44 21 67 47 65 42 61

Explanation / Answer

Here Summary of the mean and variance of all three column

Here Numerator degrees of freedom = 2

Denominator degrees of freedom = 9

(b) Here grand mean xbar-bar = 1/3 * (34.5 + 41 + 46.75) = 40.75

S2M = 4 * [(34.5 - 40.75)2 + (41 - 40.75)2 + (46.75 - 40.75)2 ] = 300.5

Square Between SEB = dF S2= 3 * [461.67 + 347.33 + 116.25] = 2775.25

- within-group population variance MSbetween = 300.5/2 = 150.25

MSwithin  = 2775.25/9 = 308.4167

- F - ration = 150.25/ 308.4167 = 0.4872

Fcrit (2,9,0.05) = 4.2565

-Here our decision is to not reject the null hypothesis and can say that there is no difference in hitting habits among professional sportsmen in the three sports

SUMMARY Groups Count Sum Average Variance Soccer Players 4 138 34.5 461.6667 Football Players 4 164 41 347.3333 Basketball Players 4 187 46.75 116.25

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