Question

use the aleks calculator to solve the following problems.
(a) consider a t distribution with 8 degrees of freedom. compute ( p(t leq 1.89) ). round your answer to at least three decimal places.
( p(t leq 1.89)=square )
(b) consider a t distribution with 17 degrees of freedom. find the value of ( c ) such that ( p(-c<t<c)=0.95 ). round your answer to at least three decimal places.
( c=square )

Explanation:

(a)

Step1: Use the t - distribution calculator

For a t - distribution with \(n = 8\) degrees of freedom, we want to find \(P(t\leq1.89)\). Using the ALEKS calculator (or a t - table/calculator function), we input the degree of freedom \(df=8\) and the value \(t = 1.89\).

Step2: Get the probability value

The calculator gives \(P(t\leq1.89)\approx0.950\)

(b)

Step1: Use the property of the t - distribution

For a t - distribution \(P(-c < t < c)=0.95\), then the area in the two tails is \(1 - 0.95=0.05\). So the area in each tail is \(\frac{1 - 0.95}{2}=0.025\)

Step2: Use the t - distribution calculator

We want to find the \(t\) - value \(c\) such that the area to the right of \(c\) is \(0.025\) with \(df = 17\). Using the ALEKS calculator (or the inverse - t function), input \(df = 17\) and the right - tail area \(0.025\). The calculator gives \(c\approx2.110\)

Answer:

(a) \(P(t\leq1.89)=0.950\)

(b) \(c = 2.110\)