Question

suppose that $chi^{2}$ follows a chi - square distribution with 19 degrees of freedom. use the aleks calculator to answer the following. (a) compute $p(chi^{2}leq11)$. round your answer to at least three decimal places. $p(chi^{2}leq11)=square$ (b) find $k$ such that $p(chi^{2}geq k)=0.025$. round your answer to at least two decimal places. $k = square$

Explanation:

Step1: Use chi - square distribution table or calculator

For part (a), use the ALEKS calculator with degrees of freedom $df = 19$ to find the cumulative distribution function value at $x = 11$. The cumulative - distribution function of a chi - square distribution $\chi^{2}(df)$ gives $P(\chi^{2}\leq x)$.

Step2: Use inverse - chi - square distribution

For part (b), use the inverse - chi - square distribution function on the ALEKS calculator. We know that the right - tailed probability $P(\chi^{2}\geq k)=0.025$ with $df = 19$. The inverse - chi - square function finds the value $k$ such that the area to the right of $k$ under the chi - square distribution curve with $df = 19$ is 0.025.

Answer:

(a) Using the ALEKS calculator, for $\chi^{2}$ with $df = 19$, $P(\chi^{2}\leq11)\approx0.109$
(b) Using the ALEKS calculator, for $\chi^{2}$ with $df = 19$ and right - tailed probability 0.025, $k\approx32.85$