Question

Find the values that form the boundaries of the critical region for a two-tailed test with a = .05 for eachof the following sample sizes:a. n = 4b. n = 15c. n = 24

Answer 1

Given

a). n = 4

b). n = 15

c). n = 24

Find

values that form the boundaries of the critical region for a two-tailed test with a = .05

Step-by-step explanation

a) n = 4

degree of freedom = n - 1 = 4 - 1 = 3

so , the t value for critical region =

`\begin{gathered} \pm t_(0.05,3) \\ \pm3.182 \end{gathered}`

b) n = 15

degree of freedom = 15 - 1 = 14

so , t- value =

`\begin{gathered} \pm t_(0.05,15) \\ \pm2.131 \end{gathered}`

c) n = 24

degree of freedom = 24 - 1 = 23

so , t - value =

`\begin{gathered} \pm t_(0.05,23) \\ \pm2.069 \end{gathered}`

Final Answer

Hence , the values that form the boundaries of the critical region for a two-tailed test with a = .05 are

a)

`\pm3.182`

b)

`\pm2.131`

c)

`\pm2.069`