iSABution the point that has probability OOS to the right is

iSABution, the point that has probability O.OS to the right is 1.645 (see the z row at the bottom of Table C for the Normal distribution the t distribution. This is an example of what we mean by the statement that t distr critical values). The value for the standard Normal distribution is smaller than the value for butions have more probability in the tails than the standard Normal. Launchpad Online Resources . The StatBoards video, How to Find t Critical Values, discusses several exam- ples of finding t critical values ledge 20.3 Critical Values. Use software or Table C to find (a) the critical value for a one-sided test with level = 0.05 based on the t(3) distribution. the critical value for a 98% confidence interval based on the t(25) distribution. (b) More Critical Values. You have an SRS of size 30 and calculate the one- sample t statistic. What is the critical value t* such that (a) t has probability 0.025 to the right of t* 20.4 (b) t has probability 0.75 to the left of t*?

Solution

20.3

If the quantity inside the parentheses is the degrees of freedom, then

a)

As it is one tailed, by table/technology, df = 3,

tcrit = 2.353363435 [ANSWER]

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b)

As this is two tailed, for 1-0.98 = 0.02 significance, df = 25,

tcrit = 2.485107175 [ANSWER]

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20.4

Here, df = n - 1 = 30 - 1 = 29.

a)

Thus, by table/technology,

t* = 2.045229642 [ANSWER]

b)

By table/technology still, as the area to the right is 1 - 0.75 = 0.25,

t* = 0.683043861 [ANSWER]