A test was made of $H _ { 0 } : \mu _ { 1 } = \mu _ { 2 } \text { versus } H _ { 1 } : \mu _ { 1 }

Question

A test was made of $H _ { 0 } : \mu _ { 1 } = \mu _ { 2 } \text { versus } H _ { 1 } : \mu _ { 1 } < \mu _ { 2 }$
The sample means were $\bar { x } _ { 1 } = 14$ and $\bar { x } _ { 2 } = 11 \text {, }$ the sample standard deviations were $s _ { 1 } = 8 \text { and } s _ { 2 } = 4$ and the sample sizes were $n _ { 1 } = 12 \text { and } n _ { 2 } = 20$
How many degrees of freedom are there for the test statistic, using the simple method?
A) 12
B) 11
C) 13
D) 10

Quizplus · Accepted Answer

The simple method for calculating degrees of freedom in a two-sample t-test, when sample variances are assumed to be unequal, is to use the smaller of $n_1 - 1$ and $n_2 - 1$. Here, $n_1 = 12$ and $n_2 = 20$, so the smaller sample size is $n_1 = 12$. Therefore, the degrees of freedom are $12 - 1 = 11$.

A Test Was Made Of H0:μ1=μ2 versus H1:μ1<μ2H _ { 0 } : \mu _ { 1 } = \mu _ { 2 } \text { versus } H _ { 1 } : \mu _ { 1 } < \mu _ { 2 }H0​:μ1​=μ2​ versus H1​:μ1​<μ2​

A Test Was Made Of $H _ { 0 } : \mu _ { 1 } = \mu _ { 2 } \text { versus } H _ { 1 } : \mu _ { 1 } < \mu _ { 2 }$