Correct option is D
To calculate the F-ratio for a one-way Analysis of Variance (ANOVA), we use the formula:
F=Mean Square Between Groups (MSb)Mean Square Within Groups (MSw)F = \frac{\text{Mean Square Between Groups (MS}_b\text{)}}{\text{Mean Square Within Groups (MS}_w\text{)}}F=Mean Square Within Groups (MSw)Mean Square Between Groups (MSb)
Step 1: Determine Degrees of Freedom · dfb=k−1df_b = k - 1dfb=k−1, where kkk is the number of groups. dfb=3−1=2df_b = 3 - 1 = 2dfb=3−1=2
· dfw=N−kdf_w = N - kdfw=N−k, where NNN is the total number of players, and kkk is the number of groups. dfw=30−3=27df_w = 30 - 3 = 27dfw=30−3=27
Step 2: Calculate Mean Squares · Mean Square Between Groups (MS
b_bb):
MSb=Sum of Squares Between Groups (SSb)dfbMS_b = \frac{\text{Sum of Squares Between Groups (SS}_b\text{)}}{df_b}MSb=dfbSum of Squares Between Groups (SSb) MSb=134.62=67.3MS_b = \frac{134.6}{2} = 67.3MSb=2134.6=67.3
· Mean Square Within Groups (MS
w_ww):
MSw=Sum of Squares Within Groups (SSw)dfwMS_w = \frac{\text{Sum of Squares Within Groups (SS}_w\text{)}}{df_w}MSw=dfwSum of Squares Within Groups (SSw) MSw=110.127≈4.074MS_w = \frac{110.1}{27} \approx 4.074MSw=27110.1≈4.074
Step 3: Calculate F-Ratio F=MSbMSwF = \frac{MS_b}{MS_w}F=MSwMSb F=67.34.074≈16.50F = \frac{67.3}{4.074} \approx 16.50F=4.07467.3≈16.50
Final Answer: The F-ratio is 16.50.
Correct Option: (d)
Additional Information: 1. The F-ratio in ANOVA indicates whether the group means differ significantly. A higher F-value suggests stronger evidence against the null hypothesis.
2. Critical values of F depend on the degrees of freedom and the significance level (e.g., α=0.05\alpha = 0.05α=0.05).
3. One-way ANOVA assumes:
· Independence of observations.
· Homogeneity of variances.
· Normally distributed groups.
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