Question

use the aleks calculator to solve the following problems.
(a) consider a t distribution with 20 degrees of freedom. compute ( p(-1.95 < t < 1.95) ). round your answer
to at least three decimal places.
( p(-1.95 < t < 1.95)=square )
(b) consider a t distribution with 27 degrees of freedom. find the value of ( c ) such that ( p(tgeq c)=0.10 ). round
your answer to at least three decimal places.
( c=square )

Explanation:

Step1: Compute \(P(-1.95 < t < 1.95)\) for \(t\) - distribution with \(20\) degrees of freedom

Since the \(t\) - distribution is symmetric, \(P(-1.95 < t < 1.95)=1 - 2P(t\geq1.95)\). Using the ALEKS calculator (or \(t\) - distribution table/software), for \(n = 20\) degrees of freedom, \(P(t\geq1.95)\) is calculated. Then \(1-2P(t\geq1.95)\) gives the result.

Step2: Find \(c\) for \(t\) - distribution with \(27\) degrees of freedom where \(P(t\geq c)=0.10\)

Using the ALEKS calculator (or \(t\) - distribution table/software) with the right - tail probability \(0.10\) and \(n = 27\) degrees of freedom. The calculator is set to the \(t\) - distribution mode, input the degrees of freedom \(27\) and the right - tail probability \(0.10\) to get the value of \(c\).

Answer:

a. \(P(-1.95 < t < 1.95)=0.949\)
b. \(c = 1.314\)