Find the critical values for the following values of the significance level $\alpha$, sample size $n$, and alternate hypothesis $H _ { 1 }$.
$$\alpha = 0.01 , n = 8 , H _ { 1 } : \mu \neq \mu _ { 0 }$$
A) -2.998, 2.998
B) -3.499, 3.499
C) -3.355, 3.355
D) -2.326, 2.326

Question

Quizplus · Accepted Answer

Given $\alpha = 0.01$ and $n = 8$, with a two-tailed test ($H_1: \mu \neq \mu_0$), we use the t-distribution because the population standard deviation is unknown and the sample size is small (n < 30). For a two-tailed test at $\alpha = 0.01$, we divide the alpha into two, leading to $\alpha/2 = 0.005$ on each tail. With $n = 8$, the degrees of freedom (df) are $n - 1 = 7$. Looking up the critical t-value for $\alpha/2 = 0.005$ and $df = 7$ in a t-table or using a calculator, we find the critical values are approximately $\pm3.499$.

Find the Critical Values for the Following Values of the Significance