Question

use the aleks calculator to solve the following problems.
(a) consider a t distribution with 15 degrees of freedom. compute ( p(-1.07 < t < 1.07) ). round your answer to at least three decimal places.
( p(-1.07 < t < 1.07)=square )
(b) consider a t distribution with 26 degrees of freedom. find the value of ( c ) such that ( p(t leq c)=0.05 ). round your answer to at least three decimal places.
( c=square )

Explanation:

Step1: Use the t - distribution property for part (a)

The \(t\) - distribution is symmetric about \(t = 0\). So, \(P(-1.07\lt t\lt1.07)=1 - 2P(t\geq1.07)\) with \(n = 15\) degrees of freedom. Using the ALEKS calculator (or a \(t\) - distribution table/software), for a \(t\) - distribution with \(n = 15\) degrees of freedom, \(P(t\geq1.07)\) is calculated.

Step2: Calculate the probability for part (a)

\(P(-1.07\lt t\lt1.07)=1-2\times0.156 = 1 - 0.312=0.688\)

Step3: Use the t - distribution for part (b)

We want to find \(c\) such that \(P(t\leq c)=0.05\) with \(n = 26\) degrees of freedom. Using the ALEKS calculator (or a \(t\) - distribution table/software) for the left - tailed \(t\) - distribution with \(n = 26\) degrees of freedom.

Answer:

(a) \(P(-1.07\lt t\lt1.07)=0.688\)
(b) \(c=-1.706\)