An F-test with 13 degrees of freedom in the numerator and 9 degrees of freedom in the denominator produced a test statistic whose value was 3.36. The null and alternate hypotheses were $H _ { 0 } : \sigma _ { 1 } = \sigma _ { 2 } \text { versus } H _ { 1 } : \sigma _ { 1 } < \sigma _ { 2 } .$
Do you reject $H _ { 0 }$ at the $\alpha = 0.05$ level?

Question

Quizplus · Accepted Answer

The p-value for this test is 0.027, which is less than 0.05, so we reject $H _ { 0 }$ at the $\alpha = 0.05$ level.

An F-Test with 13 Degrees of Freedom in the Numerator H0:σ1=σ2 versus H1:σ1<σ2.H _ { 0 } : \sigma _ { 1 } = \sigma _ { 2 } \text { versus } H _ { 1 } : \sigma _ { 1 } < \sigma _ { 2 } .H0​:σ1​=σ2​ versus H1​:σ1​<σ2​.

An F-Test with 13 Degrees of Freedom in the Numerator $H _ { 0 } : \sigma _ { 1 } = \sigma _ { 2 } \text { versus } H _ { 1 } : \sigma _ { 1 } < \sigma _ { 2 } .$