(4 points) Identify the critical t. An independent random sample is selected from an approximately normal population with unknown standard deviation. Find the degrees of freedom and the critical t value t∗ for the given sample size and confidence level. Round critical t values to 4 decimal places.

For this case the significance level is given by [tex] \alpha=1-0.9=0.1[/tex] and the [tex]\alpha/2 =0.05[/tex] and for this case we can ue the following code:

"=-T.INV(0.05,4)"

And for this case the critical value would be [tex]t_{cric}= 2.1319[/tex]

b) [tex] df =n-1= 13-1= 12[/tex]

For this case the significance level is given by [tex] \alpha=1-0.95=0.05[/tex] and the [tex]\alpha/2 =0.025[/tex] and for this case we can ue the following code:

"=-T.INV(0.025,12)"

And for this case the critical value would be [tex]t_{cric}=2.1788[/tex]

c) [tex] df =n-1= 22-1= 21[/tex]

For this case the significance level is given by [tex] \alpha=1-0.98=0.02[/tex] and the [tex]\alpha/2 =0.01[/tex] and for this case we can ue the following code:

"=-T.INV(0.01,21)"

And for this case the critical value would be [tex]t_{cric}=2.5176 [/tex]

d) [tex] df =n-1= 15-1= 14[/tex]

For this case the significance level is given by [tex] \alpha=1-0.99=0.01[/tex] and the [tex]\alpha/2 =0.005[/tex] and for this case we can ue the following code:

"=-T.INV(0.005,14)"

And for this case the critical value would be [tex]t_{cric}=2.9768 [/tex]

Step-by-step explanation:

Part a

n = 5 , Conf. =0.90

For this case the degrees of freedom are given by:

[tex] df =n-1= 5-1= 4[/tex]

For this case the significance level is given by [tex] \alpha=1-0.9=0.1[/tex] and the [tex]\alpha/2 =0.05[/tex] and for this case we can ue the following code:

"=-T.INV(0.05,4)"

And for this case the critical value would be [tex]t_{cric}= 2.1319[/tex]

Part b

n = 13 , Conf. =0.95

For this case the degrees of freedom are given by:

[tex] df =n-1= 13-1= 12[/tex]

For this case the significance level is given by [tex] \alpha=1-0.95=0.05[/tex] and the [tex]\alpha/2 =0.025[/tex] and for this case we can ue the following code:

"=-T.INV(0.025,12)"

And for this case the critical value would be [tex]t_{cric}=2.1788[/tex]

Part c

n = 22 , Conf. =0.98

For this case the degrees of freedom are given by:

[tex] df =n-1= 22-1= 21[/tex]

For this case the significance level is given by [tex] \alpha=1-0.98=0.02[/tex] and the [tex]\alpha/2 =0.01[/tex] and for this case we can ue the following code:

"=-T.INV(0.01,21)"

And for this case the critical value would be [tex]t_{cric}=2.5176 [/tex]

Part d

n = 15 , Conf. =0.99

For this case the degrees of freedom are given by:

[tex] df =n-1= 15-1= 14[/tex]

For this case the significance level is given by [tex] \alpha=1-0.99=0.01[/tex] and the [tex]\alpha/2 =0.005[/tex] and for this case we can ue the following code:

"=-T.INV(0.005,14)"

And for this case the critical value would be [tex]t_{cric}=2.9768 [/tex]