$$\mathrm { H } _ { \mathrm { a } } : \sigma _ { 1 } ^ { 2 } \neq \sigma _ { 2 } ^ { 2 } ; \alpha = 0.10 , \mathrm { n } _ { 1 } = 10 , \mathrm { n } _ { 2 } = 16$$
Assume that $\mathrm { s } _ { 2 } ^ { 2 } \mathrm { s } 2$.
A) $F 3.01$
B) $| F | 2.34$
C) $F 2.59$
D) $| \mathrm { F } | 2.59$

Question

$$\mathrm { H } _ { \mathrm { a } } : \sigma _ { 1 } ^ { 2 } \neq \sigma _ { 2 } ^ { 2 } ; \alpha = 0.10 , \mathrm { n } _ { 1 } = 10 , \mathrm { n } _ { 2 } = 16$$
Assume that $\mathrm { s } _ { 2 } ^ { 2 } > \mathrm { s } 2$.
A) $F > 3.01$
B) $| F | > 2.34$
C) $F > 2.59$
D) $| \mathrm { F } | > 2.59$

Quizplus · Accepted Answer

Given the null hypothesis $H_a: \sigma_1^2 \neq \sigma_2^2$, we are dealing with a two-tailed test for variance. The correct choice involves comparing the F statistic to a critical value from the F-distribution table. Since $s_2^2 > s_1^2$ is assumed, we directly compare $F$ to a critical value for a given significance level ($\alpha = 0.10$) and degrees of freedom ($n_1 - 1 = 9$ and $n_2 - 1 = 15$). The correct critical value for these parameters is indeed greater than 3.01, making choice A correct. Choices involving absolute values of $F$ or incorrect critical values are not applicable for this specific hypothesis test setup.

Assume That s22>s2\mathrm { s } _ { 2 } ^ { 2 } > \mathrm { s } 2s22​>s2

Assume That $\mathrm { s } _ { 2 } ^ { 2 } > \mathrm { s } 2$