Question

Complete parts ​(a) through ​(c) below.

a) Determine the critical​ value(s) for a​ right-tailed test of a population mean at the α = 0.10 level of significance with 15 degrees of freedom.
​b) Determine the critical​ value(s) for a​ left-tailed test of a population mean at the α = 0.10 level of significance based on a sample size of n = 20.
c) Determine the critical​ value(s) for a​ two-tailed test of a population mean at the α = 0.05 level of significance based on a sample size of n = 18.

Answer 1

Answer:

a) $t_{crit}=1.34$

b) $t_{crit}=-1.33$

c) $t_{crit}=\pm 2.11$

Step-by-step explanation:

Part a

$\alpha=0.1$ represent the significance level

df =15

Since is a right tailed test the critical value is given by:

$t_{crit}=1.34$

And we can use the following excel code to find it: "=T.INV(0.9,15)"

Part b

$\alpha=0.1$ represent the significance level

n=20 represent the sample size

First we need to find the degrees of freedom given by:

$df=n-1=20-1=19$

Since is a left tailed test the critical value is given by:

$t_{crit}=-1.33$

And we can use the following excel code to find it: "=T.INV(0.1,19)"

Part c

$\alpha=0.05$ represent the significance level

n=18 represent the sample size

First we need to find the degrees of freedom given by:

$df=n-1=18-1=17$

The value of $\alpha=0.05$ and $\alpha/2 =0.025$

Since is a two tailed tailed we have two critical values is given by:

$t_{crit}=\pm 2.11$

And we can use the following excel code to find it: "=T.INV(0.025,17)"