If $\alpha=0.10$, the hypothesis that $\sigma_{1}=\sigma_{2}$, the sample variances $s_{1}^{2}=18$ and $s_{2}^{2}=54$ were obtained, based on sample sizes of $n_{1}=15$ and $n_{2}=10$ respectively, the null hypothesis should be
A) rejected since $F=3$.
B) not rejected since $F=3$.
C) rejected since $F=0.33$.
D) not rejected since $F=0.33$.

Question

Quizplus · Accepted Answer

The calculated F-value is 3, and comparing it with the critical F-value at $\alpha=0.10$ for degrees of freedom $df_1=14$ and $df_2=9$, the null hypothesis should be rejected.

If α=0.10\alpha=0.10α=0.10 , the Hypothesis That σ1=σ2\sigma_{1}=\sigma_{2}σ1​=σ2​ , the Sample Variances s12=18s_{1}^{2}=18s12​=18 And s22=54s_{2}^{2}=54s22​=54

If $\alpha=0.10$ , the Hypothesis That $\sigma_{1}=\sigma_{2}$ , the Sample Variances $s_{1}^{2}=18$ And $s_{2}^{2}=54$