Question

confidence intervals and hypothesis testing
introduction to finding the value that cuts off a given area under the cur...
a chi - square distribution with 11 degrees of freedom is graphed below. the region under the curve to the right of $\chi_{0.15}^{2}$ is shaded. the area of this region is
0.15.
find the value of $\chi_{0.15}^{2}$. round your answer to three decimal places.
$\chi_{0.15}^{2}=\square$

Explanation:

Step1: Use the chi - square distribution table or a statistical software

We know that for a chi - square distribution \(\chi^{2}_{\alpha,df}\), where \(\alpha = 0.15\) and \(df=11\).

Step2: Look up the value

Using a chi - square distribution table (or a calculator with a chi - square inverse function, for example, in R: qchisq(0.85, 11, lower.tail = TRUE) or in Excel: CHISQ.INV.RT(0.15,11)).

Answer:

\(17.275\)