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Chapter 11: Problem 5

Determine the value of \(\chi^{2}\) for 23 degrees of freedom and an area of \(.990\) in the left tail of the chisquare distribution curve.

Short Answer

Expert verified
Normally the solution would be found from a chi-square distribution table. Unfortunately, for this particular exercise, you would need a computer software or online calculator that can calculate chi-square values because common statistical tables (which goes step by step, for example from 0.005 to 0.995 with steps of 0.005) do not have values for an area of 0.990 in the left tail for 23 degrees of freedom.

Step by step solution

01

Understand the chi-square distribution

The chi-square distribution is a theoretical probability distribution that's applicable to the sample variances in hypothesis testing. It is heavily skewed to the right and although it's defined for all positive numbers, it's only used for integer degrees of freedom.
02

Using the chi-square distribution table

The chi-square distribution table is tabulated according to the degrees of freedom. Each row represents a degree of freedom, and the columns represent the area to the right of the \(\chi^{2}\) value. In this case, the area to the left of the \(\chi^{2}\) value is given, hence you look at the complement value which is \(1 - .990 = 0.01\) of the area to the right of the \(\chi^{2}\) value.
03

Finding the chi-square value

To find the \(\chi^{2}\) value given the degree of freedom (23 in this case) and the area to the right of the \(\chi^{2}\) value (.01 in this case), you locate the row in the table that corresponds to 23 degrees of freedom, and then find the column that is closest to but does not exceed .01. The point of intersection gives the \(\chi^{2}\) value.

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Most popular questions from this chapter

Find the value of \(\chi^{2}\) for 28 degrees of freedom and an area of \(.05\) in the right tail of the chi-square distribution curve.

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