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Determine the t-value in each of the cases. Click the icon to view the table of areas under the t-distribution. (a) Find the
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Solution:

Part a)

df = 18 , area in right tail = 0.005

t distribution critical values Upper-tail probability p 15 df 25 .20 .10 .05 .025 .02 .01 005 66.66 925 1.841 .604 .032 .707

t critical value = 2.878

Part b)

df =18

Area in right tail = 0.20

t distribution critical values Upper-tail probability p 20 15 df 25 .05 .025 .02 .01 .005 .10 1376 1.61 0.78 0.941 0.920 0.06

t critical value = 0.862

Part c)

df = 24

Area in left tail = 0.02

Since t table gives t values for right area, we use symmetry that t critical values are same for left and right area with different signs.

That is we look for df = 24 and right tail area = 0.02 and find t critical value

Since we need t value for left tail, we use negative sign.

thus

t distribution critical values Upper-tail probability p df 25 .20 .15 .05 .025 .02 .01 .10 6.89 4.849 3482 2999 2.57 2. 12 2.

t critical value = -2.172

Part d)

df = 9

c = confidence level = 50% = 0.50

then level of significance = \alpha = 1 - c = 1 - 0.5 = 0.5

thus find right tail area = \alpha /2 = 0.5 / 2 = 0.25

t distribution critical values Upper-tail probability p df 25 .15 .10 .05 .025 .02 .01 .20 1.000 0.16 0. 65 0.41 0. 27 0. 18

t critical value = 0.703

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