The Chi-Square Distribution

According to the facts about the Chi-Square distribution, what is the population mean (μ) and population standard deviation (σ) if the degrees of freedom (df) are 25?

What is a key characteristic of the Chi-square curve's shape?

In a test of a single variance, what is the primary assumption about the underlying distribution of the data?

A SCUBA instructor believes the standard deviation for his students' dive depths is three feet. His assistant thinks the standard deviation is less than three feet. What would be the correct null (H0) and alternative (Ha) hypotheses for a test?

What is the primary purpose of a goodness-of-fit test?

What is the formula for the degrees of freedom (df) in a goodness-of-fit test?

In Example 11.4, regarding student absenteeism, why was it necessary to combine the '9-11' and '12+' absence categories before conducting the goodness-of-fit test?

What is the null hypothesis (H0) for a test of independence?

How are the degrees of freedom calculated for a test of independence using a contingency table?

In Example 11.9, a study of volunteers is conducted. The contingency table has 3 rows (types of volunteer) and 3 columns (hours volunteered). What are the degrees of freedom for this test of independence?

What is the key difference between a test of homogeneity and a test of independence?

In a test for homogeneity involving a comparison of living arrangements between men and women college students (Example 11.11), there are 4 categories of living arrangements. What are the degrees of freedom?

What is the null hypothesis (H0) for a test of homogeneity?

When does the Chi-square curve approximate a normal distribution?

In the test of independence example for speeding violations and cell phone use (Example 11.8), what is the expected number of drivers who used a cell phone while driving and received a speeding violation, assuming independence?

For the chi-square tests discussed in Chapter 11 (goodness-of-fit, independence, homogeneity), what is the minimum required expected value for each cell?

In Example 11.5, a goodness-of-fit test is performed on employee absences. The calculated chi-square test statistic is 3. With 4 degrees of freedom and a significance level of 0.05, the critical value is 9.48. What is the correct decision?

The test statistic for a goodness-of-fit test, a test of independence, and a test for homogeneity are all based on what core concept?

If a chi-square test for independence between two factors yields a very large test statistic that falls in the right tail of the distribution, what can be concluded?

In a study of 420,019 cell phone users, 172 developed brain cancer. The rate for non-cell phone users is 0.0340 percent. What is the null hypothesis (H0) to test if the cancer rate for cell phone users is greater?

In Example 11.3, Professor Holmes tests the variance of donut filling. This is set up as a two-tailed test. Why?

The Bureau of Labor Statistics gathers data on employment. A sample is taken across several industry sectors in the years 2000, 2010, and 2020. What type of chi-square test would be appropriate to see if the distribution of jobs across industries is dependent on the year?

A math teacher wants to see if two of their classes have the same distribution of test scores. What is the most appropriate chi-square test to use?

What does a test statistic value of zero for a chi-square test imply?

If a chi-square distribution has a df = 2, its shape is similar to which other distribution?

In a contingency table for a test of independence with 4 rows and 5 columns, what are the degrees of freedom?

Which of the following chi-square tests typically involves data from two different populations?

In the goodness-of-fit example with streaming services (Example 11.6), the sample consists of 600 families. The expected percentage of families with 0 services is 10 percent. What is the expected frequency for this category?

What is the general direction of all chi-square tests for goodness-of-fit, independence, and homogeneity?

If you are testing whether the marital status distribution of young adult males (ages 18-24) fits the distribution of the entire U.S. male population, what type of test should be used?

In a study of smokers in California and Hawaii, data is collected on ethnicity and smoking level per day. What is the appropriate test to determine if smoking level is dependent on ethnicity?

In the test of independence for volunteer hours vs. volunteer type (Example 11.9), the calculated chi-square statistic is 12.99. With df=4 and a 5 percent significance level, the critical value is 9.488. What is the correct conclusion?

A study on student absenteeism (Example 11.4) originally had 5 categories. After combining two categories to meet the minimum expected frequency rule, how many degrees of freedom remained for the test?

If a chi-square test of a single variance is conducted and the test statistic falls in the left tail, what does this suggest about the sample variance compared to the hypothesized population variance?

Which statement accurately describes the relationship between the three main chi-square tests discussed in Chapter 11?

What is the alternative hypothesis (Ha) for a goodness-of-fit test?

In a chi-square test, if the observed frequencies are very close to the expected frequencies, what would you expect the chi-square test statistic to be?

A test of a single variance has df = 24. A student is performing a right-tailed test. Which value from a chi-square table would be the critical value for a 5 percent significance level?

Which of the following scenarios would be best analyzed using a test of a single variance?

If the null hypothesis for a test of independence is rejected, what can be concluded?

A test for homogeneity is planned to compare the distribution of car types (sport, sedan, etc.) for families and singles. There are 5 types of cars. What are the degrees of freedom for this test?

What is the key similarity between a test of independence and a test for homogeneity?

In a goodness-of-fit test, if the p-value is 0.0113 and the significance level is 0.05, what is the correct decision?

For a chi-square distribution with df=24, where is the mean located?

A plant manager is concerned that their equipment may need recalibrating because the standard deviation of cereal box weights should be at most 0.5 oz. A sample of 84 boxes had a standard deviation of 0.54 oz. What is the correct alternative hypothesis (Ha) for this test?

In a goodness-of-fit test for a fair six-sided die rolled 120 times, what is the expected frequency for each face value?

In a test of independence for travel distance and ticket class (Chapter 11 Homework), how do you calculate the expected number of passengers who travel 201-300 miles and purchase second-class tickets?

If a chi-square test for homogeneity results in a failure to reject the null hypothesis, what is the appropriate conclusion?

What does it mean for a chi-square test statistic to be 'always greater than or equal to zero'?

In the study comparing Ivy League application acceptance types (Homework Problem 2), what type of test would be used to determine if the distribution of accepted students is the same for both regular and early decision applicants?