Exam 13: Chi-Square Tests

Consider the 3 × 2 contingency table below. How many degrees of freedom are associated with the chi-square test?

A contingency table summarizes data that has been classified into two dimensions or scales.

In a contingency table, if all of the expected frequencies equal the observed frequencies, then we can conclude that there is a perfect association between rows and columns.

A survey was conducted on the age and gender of the purchasers of a specific automotive model. The results are below. For each row total, calculate the corresponding percentage.

On the most recent tax cut proposal, a random sample of Democrats and Republicans in the Congress cast their votes as follows. Use a significance level of .01 and determine whether the opinions on the tax cut proposal and the party affiliation are independent.

In performing a chi-square goodness-of-fit test with multinomial probabilities, the ________ the difference between observed and expected frequencies, the higher the probability of concluding that the probabilities specified in the null hypothesis are favored over the alternative hypothesis.

The following frequency table summarizes the ages of 60 shoppers at the local farmer's market. The estimated mean is 36.25, and the estimated standard deviation is 13.57. Calculate the value of the chi-square test statistic to determine whether these measurements came from a normal population.

A paper presented at a recent meeting of higher education researchers compared the type of college freshmen attend and the numbers who drop out. A random sample of freshmen shows the following results. Calculate the chi-square statistic for this test of independence.

The chi-square distribution is a continuous probability distribution that is skewed to the left.

On the most recent tax cut proposal, a random sample of Democrats and Republicans in the Congress cast their votes as follows. Determine the expected frequencies for both the Democrats and Republicans who favor the tax cut proposal for the chi-square test of independence.

A human resource manager is interested in whether absences occur during the week with equal frequency. The manager took a random sample of 100 absences and created the following table. How many degrees of freedom are associated with the chi-square test? Use α = .05 and determine the rejection point condition of the chi-square statistic.

A paper presented at a recent meeting of higher education researchers compared the type of college that freshmen attend and the numbers who drop out. A random sample of freshmen shows the following results. Determine the expected frequencies for the two cells of 4-year public institutions that will be used in the chi-square test of independence.

A manufacturing company produces part QV2Y for the aerospace industry. This particular part can be manufactured using 3 different production processes. The management wants to know if the quality of the units of part QV2Y is the same for all three processes. The production supervisor obtained the following data: Process 1 had 29 defective units in 240 items, Process 2 produced 12 defective units in 180 items, and Process 3 manufactured 9 defective units in 150 items. At a significance level of 0.05, we performed a chi-square test of independence to determine if the quality of the items produced appears to be independent of the production process. What are the degrees of freedom for the chi-square statistic?

The actual counts in the cells of a contingency table are referred to as the expected cell frequencies.

When we carry out a chi-square test of independence, the chi-square statistic is based on degrees of freedom, where r and c denote, respectively, the number of rows and columns in the contingency table.

The HR manager of a major office supply chain is interested in determining whether employee educational level affects knowledge of their job. An exam was given to 120 employees. The results are below. For each cell, calculate the corresponding cell, row, and column percentage.

An experiment consists of 400 observations and four mutually exclusive groups. If the probability of a randomly selected item being classified into any of the four groups is equal, then the expected number of items that will be classified into group 1 is ________.

A real estate company is analyzing the selling prices of residential homes in a given community. 140 homes that have been sold in the past month are randomly selected and their selling prices are recorded. The statistician working on the project has stated that in order to perform various statistical tests, the data must be distributed according to a normal distribution. In order to determine whether the selling prices of homes included in the random sample are normally distributed, the statistician divides the data into 6 classes of equal size and records the number of observations in each class. She then performs a chi-square goodness-of-fit test for normal distribution. The results are summarized in the following table. Goodness-of-Fit Test At a significance level of .05, we

AAA Co. operates distribution centers in the Midwest. Three of their centers were recently audited to determine if they are in compliance with company standard billing procedures. According to the auditing firm, a billing had an equal probability of being from each of the three centers. A random sample of the audited billings had the following distribution. Center 1: 385 billings Center 2: 305 billings Center 3: 210 billings Calculate the goodness of fit and determine whether H₀ should be rejected at α = .01.

The number of degrees of freedom associated with a chi-square test for independence based upon a contingency table with 4 rows and 3 columns is ________.