The F statistic from an experiment with K equals three and N equals 50s 3.67 at a equals 0.05 Will you reject the no hypothesis
The Correct Answer and Explanation is:
To determine whether we reject the null hypothesis based on the given information, we need to compare the calculated F-statistic to the critical F-value from an F-distribution table.
Step-by-Step Approach:
- Given Data:
- F-statistic: 3.67
- Number of groups (K): 3
- Sample size (N): 50
- Significance level (α): 0.05
- Degrees of Freedom:
- Degrees of freedom for the numerator (between groups) = K−1=3−1=2K – 1 = 3 – 1 = 2K−1=3−1=2
- Degrees of freedom for the denominator (within groups) = N−K=50−3=47N – K = 50 – 3 = 47N−K=50−3=47
- Find the Critical F-Value:
Using an F-distribution table or a statistical calculator for α=0.05\alpha = 0.05α=0.05, we look up the critical value for F0.05,2,47F_{0.05, 2, 47}F0.05,2,47, where 2 is the degrees of freedom for the numerator and 47 is the degrees of freedom for the denominator. The critical F-value for α=0.05\alpha = 0.05α=0.05, df1=2df_1 = 2df1=2, and df2=47df_2 = 47df2=47 is approximately 3.22. - Decision Rule:
- If the calculated F-statistic is greater than the critical F-value, we reject the null hypothesis.
- If the calculated F-statistic is less than or equal to the critical F-value, we fail to reject the null hypothesis.
- Comparison:
- The calculated F-statistic is 3.67.
- The critical F-value at α=0.05\alpha = 0.05α=0.05 is 3.22.
- Since 3.67 > 3.22, we reject the null hypothesis.
Conclusion:
We reject the null hypothesis because the calculated F-statistic (3.67) exceeds the critical value (3.22) at a significance level of 0.05. This indicates that there are statistically significant differences between the groups in the experiment.
