Question

check here for instructional material to complete this problem. evaluate the formula $\chi^{2}=\frac{(n - 1)s^{2}}{\sigma^{2}}$ when $\sigma = 2.51$, $n = 41$, and $s = 2.84$. $\chi^{2}=\square$ (round to three decimal places as needed.)

Explanation:

Step1: Substitute the values into the formula

Substitute \(n = 41\), \(s=2.84\), \(\sigma = 2.51\) into \(\chi^{2}=\frac{(n - 1)s^{2}}{\sigma^{2}}\).
First, calculate \(n-1\): \(n-1=41 - 1=40\).
Then, calculate \(s^{2}\): \(s^{2}=(2.84)^{2}=8.0656\).
And \(\sigma^{2}=(2.51)^{2}=6.3001\).
The formula becomes \(\chi^{2}=\frac{40\times8.0656}{6.3001}\).

Step2: Calculate the numerator

Calculate \(40\times8.0656\): \(40\times8.0656 = 322.624\).
The formula is now \(\chi^{2}=\frac{322.624}{6.3001}\).

Step3: Calculate the final value

\(\chi^{2}=\frac{322.624}{6.3001}\approx51.209\) (using a calculator for the division \(322.624\div6.3001\)).

Answer:

\(51.209\)