An $F$-test with 10 degrees of freedom in the numerator and 5 degrees of freedom in the denominator produced a test statistic whose value was $10.07$. The null and alternate hypotheses were $H _ { 0 } : \sigma _ { 1 } = \sigma _ { 2 }$ versus $H _ { 1 } : \sigma _ { 1 }

Question

An $F$-test with 10 degrees of freedom in the numerator and 5 degrees of freedom in the denominator produced a test statistic whose value was $10.07$. The null and alternate hypotheses were $H _ { 0 } : \sigma _ { 1 } = \sigma _ { 2 }$ versus $H _ { 1 } : \sigma _ { 1 } < \sigma _ { 2 }$.
Do you reject $H _ { 0 }$ at the $\alpha = 0.01$ level?

Quizplus · Accepted Answer

The test statistic of $10.07$ corresponds to a p-value of approximately $0.0005$, which is less than the significance level of $\alpha=0.01$. Therefore, we reject the null hypothesis and conclude that there is sufficient evidence to support the alternate hypothesis that $\sigma_1<\sigma_2$.

An FFF -Test with 10 Degrees of Freedom in the Numerator and Numerator

An $F$ -Test with 10 Degrees of Freedom in the Numerator and Numerator