For a random variable T that is T22 distributed as a statist

For a random variable T that is T(22) distributed as a statistical package or a table to find

a. Pr[T>2.0]

b. Pr[T<-2.0 or T>2.0]

c. t* such that Pr[T>t*]=0.05

d. t* such that Pr[T<t* or T>t*] = 0.05

Solution

If you want to use Excel, you can use the T.DIST(t, df, 1) function to get the left tailed area of a t score.

a)

Pr(T > 2.0) = 1 - Pr(T < 2.0)

=1 - T.DIST(2.0, 22, 1)

= 0.028997851 [ANSWER]

b)

P(T < -2.0 or T>2.0) = 2 P(T < -2.0) , by symmetry.

Thus,

P(T < -2.0 or T>2.0) = 2 P(T < -2.0)

= 2*T.DIST(-2.0, 22, 1)

= 0.057995702 [ANSWER]

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Here, you can use T.INV(left tailed area, df) to get t*.

c)

=T.INV(1-0.05, 22)

t* = 1.717144374 [answer]

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d)

Here, maybe you meant

t* such that Pr[T<-t* or T>t*] = 0.05

In that case, the left tailed area of -t is 0.05/2,

-t*:

=T.INV(0.05/2, 22)

-t* = -2.073873068

t* = 2.073873068 [ANSWER]