Question

suppose that $chi^{2}$ follows a chi - square distribution with 17 degrees of freedom. use the aleks calculator to answer the following. (a) compute $p(chi^{2}leq26)$. round your answer to at least three decimal places. $p(chi^{2}leq26)=0.922$ (b) find $k$ such that $p(chi^{2}geq k)=0.025$. round your answer to at least two decimal places. $k = 30.19$

Explanation:

Step1: Use chi - square distribution table or calculator

For part (a), we use a chi - square distribution calculator (like ALEKS) with degrees of freedom $df = 17$. We input the value $x = 26$ to find $P(\chi^{2}\leq26)$. The calculator directly gives the cumulative probability value.

Step2: Use inverse - chi - square distribution

For part (b), we know that $P(\chi^{2}\geq k)=0.025$. This is equivalent to $P(\chi^{2}

Answer:

(a) $P(\chi^{2}\leq26)=0.922$
(b) $k = 30.19$