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Chapter 11: Problem 2

Find the value of \(\chi^{2}\) for 12 degrees of freedom and an area of \(.025\) in the right tail of the chi-square distribution curve.

Short Answer

Expert verified
Given the provided degrees of freedom and tail area, the critical \(\chi^2\) value can be found from a chi-square table. Exact value might vary depending on the scale and accuracy of the chosen Chi-square table. However, using most standard Chi-square tables, the \(\chi^2\) value for 12 degrees of freedom and an area of 0.025 in the right tail is approximately 21.03.

Step by step solution

01

Understand the $\chi^{2}$ table

The chi-square table usually lists the degrees of freedom in the first column and the tail areas or significance levels in the first row. The body of the table contains the critical chi-square values that correspond to the specific degrees of freedom and tail areas.
02

Locate the degrees of freedom

The problem states that there are 12 degrees of freedom. To identify the critical value, find the row that corresponds to 12 degrees of freedom. In the chi-square table, this usually is quite simple as the degrees of freedom are most commonly listed in ascending order.
03

Locate the significance level or tail area

The problem also states that the tail area is \(0.025\). Find this value from the top row of the chi-square table. Once both the degrees of freedom and the tail area are found, identify the value that lies at the intersection of the appropriate row and column. This value is the critical chi-square value.

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Most popular questions from this chapter

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