Find the Critical Value or Values Of $\chi ^ { 2 }$

question 18

Multiple Choice

Find the critical value or values of $\chi ^ { 2 }$ based on the given information.
-For large numbers of degrees of freedom, the critical $\chi ^ { 2 }$ values can be approximated as follows:
$$\chi ^ { 2 } = \frac { 1 } { 2 } ( z + \sqrt { 2 k - 1 } ) ^ { 2 }$$ where $k$ is the number of degrees of freedom and $z$ is the critical value. To find the lower critical value, the negative $z$ -value is used, to find the upper critical value, the positive $z$ -value is used. Use this approximation to estimate the critical value of $\chi ^ { 2 }$ in a two-tailed hypothesis test with $\mathrm { n } = 104$ and $\alpha = 0.10$ .

• A) \(\chi ^ { 2 } \approx 84.992\) and \(\chi ^ { 2 } \approx 121.646\)
• B) \(\chi ^ { 2 } \approx 80.300\) and \(\chi ^ { 2 } \approx 127.406\)
• C) \(\chi ^ { 2 } \approx 81.186\) and \(\chi ^ { 2 } \approx 128.520\)
• D) \(\chi ^ { 2 } \approx 85.903\) and \(\chi ^ { 2 } \approx 122.735\)

---

Definitions:

Law Passed

The successful enactment of a bill into law after it has been approved by the legislative body and, usually, the head of the government.

Closed Primary

A type of primary election where only registered party members can vote to choose their party's candidates.

Open Primary

A primary election where voters are not required to declare party membership to vote for their preferred candidate for a public office.

Majority System

A voting system in which a candidate or proposition must receive more than half of the votes to win.