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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
The chi-square value for 12 degrees of freedom and an area of .025 in the right tail of the chi-square distribution curve is approximately 21.03 according to the Chi-square table. This value might differ slightly depending on the exact chi-square table used.

Step by step solution

01

Understanding Chi-Square distribution

The chi-square distribution, sometimes called the chi-squared distribution, is a family of distributions that take only non-negative values. It is used in hypothesis testing and is derived from the Gaussian distribution. Chi-square distribution plays a crucial role in statistical inference where it is used in the goodness of fit and test of independence.
02

Locating Degrees of Freedom in Chi-Square distribution table

In the Chi-Square table, locate the row for 12 degrees of freedom. These are usually listed down the left-hand side of the table.
03

Locating the Chi-Square Value

Since we want the area in the right tail of .025, we locate this value at the top of the chi-square distribution table. Where this column intersects with your degrees of freedom row is where you will find your chi-square value.

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Most popular questions from this chapter

The October 2011 ISACA Shopping on the Job Survey asked employees, "During the holiday season (November and December), how much total time do you think an average employee at your enterprise spends shopping online using a work- supplied computer or smartphone?" Among those who responded, \(3 \%\) said 0 hours, \(24 \%\) said 1 to 2 hours, \(22 \%\) said 3 to 5 hours, and \(51 \%\) said 6 or more hours (www.isaca. org/SiteCollectionDocuments/2011-ISACA-Shopping- on-the-Job-Survey-US.pdf). Suppose that another poll conducted recently asked the same question of 215 randomly selected business executives, which produced the frequencies listed in the following table. $$ \begin{array}{l|cccc} \hline \text { Response/category } & 0 \text { hours } & 1-2 \text { hours } & 3-5 \text { hours } & 6 \text { or more hours } \\ \hline \text { Frequency } & 2 & 41 & 55 & 117 \\ \hline \end{array} $$ Test at a \(2.5 \%\) significance level whether the distribution of responses for the executive survey differs from that of October 2011 survey of employees.

Determine the value of \(\chi^{2}\) for 13 degrees of freedom and a. 025 area in the left tail of the chi-square distribution curve b. \(.995\) area in the right tail of the chi-square distribution curve

A sample of 30 observations selected from a normally distributed population produced a sample variance of \(5.8\). a. Write the null and alternative hypotheses to test whether the population variance is different from \(6.0\) b. Using \(\alpha=.05\), find the critical value of \(\chi^{2} .\) Show the rejection and nonrejection regions on a chi-square distribution curve. c. Find the value of the test statistic \(\chi^{2}\). d. Using a \(5 \%\) significance level, will you reject the null hypothesis stated in part a?

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