Find the critical values for the following values of the significance level $\alpha$ sample size n , and alternate hypothesis $H _ { 1 }$
$\alpha = 0.05 , n = 11 , H _ { 1 } : \mu \neq \mu _ { 0 }$
A) -1.645,1.645
B) -2.228,2.228
C) -2.201,2.201
D) -1.812,1.812

Question

Find the critical values for the following values of the significance level  $\alpha$ sample size  n , and alternate hypothesis $H _ { 1 }$
$\alpha = 0.05 , n = 11 , H _ { 1 } : \mu \neq \mu _ { 0 }$
A)  -1.645,1.645 
B)  -2.228,2.228 
C)  -2.201,2.201 
D)  -1.812,1.812

Quizplus · Accepted Answer

Given $\alpha = 0.05$, $n = 11$, and a two-tailed test ($H_1: \mu \neq \mu_0$), we use the t-distribution because the sample size is small (n < 30). The degrees of freedom (df) are $n - 1 = 10$. For a two-tailed test with $\alpha = 0.05$, we look up the critical t-value for 10 degrees of freedom at $\alpha/2 = 0.025$ in each tail, which gives us approximately $\pm2.228$.

Find the Critical Values for the Following Values of the Significance