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Chapter 11: Problem 3

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.

Short Answer

Expert verified
Check the Chi-Square table for 28 degrees of freedom and an upper-tail probability of 0.05, the exact value may vary slightly based on the specific table used. The Ackland's Statistical Tables generally lists this value as ~38.33.

Step by step solution

01

Understand the Problem

In this problem, a value from a chi-square distribution is needed. The chi-square distribution is used in statistics to represent the distribution of a sum of the squares of k independent standard normal random variables. Here, the degree of freedom (df) represents the number of independent variables involved, and is given as 28. The area in the right tail is 0.05, this is the probability that a variable from this distribution can hold a value that is equal to or greater than the chi-square value we want to find.
02

Reference Chi-Square Table

There isn't a formula for directly calculating chi-square values. Instead, statisticians typically reference tables which list chi-square values against degrees of freedom for various tail area probabilities. These tables are derived from the chi-square distribution function.
03

Find Value using Table

Looking at the Chi-Square table, find the row for 28 degrees of freedom. Moving horizontally along that row, find the column where the upper-tail probability is approximately 0.05. The value at the intersection of this row and column is the desired chi-square value.

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Most popular questions from this chapter

To make a test of independence or homogeneity, what should be the minimum expected frequency for each cell? What are the alternatives if this condition is not satisfied?

Each of five boxes contains a large (but unknown) number of red and green marbles. You have been asked to find if the proportions of red and green marbles are the same for each of the five boxes. You sample 50 times, with replacement, from each of the five boxes and observe \(20,14,23,30\), and 18 red marbles, respectively. Can you conclude that the five boxes have the same proportions of red and green marbles? Use a \(.05\) level of significance.

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