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# Confidence intervals for one population mean when S.D. is unknown /t-curve

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For a t-curve with df = 8, find each t-value and illustrate your results graphically.

a.The t-value having area 0.05 to its right.
b. t 0.10
c.The t-value having area 0.01 to its left
(hint: A t-curve is symmetric about 0.)
d.The two t-values that divide the area under the curve into a middle 0.95 area and two outside 0.025 areas

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#### Solution Preview

please refer to the attachment for graphs

a.

X
0.05
t*=1.860
Pr(X<=t*)=1-0.05=0.95, and is a one-tailed distribution, with df=8
From the t-table, t*(8, 0.95) = 1.860

b. It's not clear in your posting what is t0.10, I will take it as the t-value having area 0.10 to its ...

#### Solution Summary

For a t-curve with df = 8, find each t-value and illustrate your results graphically.

a.The t-value having area 0.05 to its right.
b. t 0.10
c.The t-value having area 0.01 to its left
(hint: A t-curve is symmetric about 0.)
d.The two t-values that divide the area under the curve into a middle 0.95 area and two outside 0.025 areas

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