Exam 13: Chi-Square Tests

When we carry out a chi-square test of independence, in the alternative hypothesis we state that the two classifications are statistically independent.

The distance (in thousands of miles) traveled by buses before their first major motor failure is distributed below, with an estimated mean and standard deviation of 95.7 and 38.1. Also shown are the expected frequencies of these intervals if the original population was a normal distribution. What is the df for testing the hypothesis that the original population is a normal distribution?

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 column total, calculate the corresponding percentage.

Consider the 3 × 2 contingency table below. Compute the expected frequencies in row 2.

Consider a set of 50 measurements with mean 50.2 and standard deviation 18.7 and with the following observed and expected frequencies. It is desired to test whether these measurements came from a normal population. At a significance level of .05, test H₀: the set of 50 measurements came from a normal population.

The following frequency table summarizes the ages of 60 shoppers at the local farmer's market. The estimated mean is 36.25, and estimated standard deviation is 13.57. Calculate the expected frequency for each interval, assuming a normal distribution.

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. It is desired to test whether these measurements came from a normal population. At a significance of .01, test H₀: the sample of 60 shoppers came from a normal population.

The chi-square goodness-of-fit test for multinomial probabilities with 5 categories has ________ degrees of freedom.

Consider a set of 50 measurements with mean 50.2 and standard deviation 18.7 and with the following observed frequencies. It is desired to test whether these measurements came from a normal population. Calculate the expected frequency for the interval 0 − 39.99.

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 What is the appropriate null hypothesis?

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 .05, the management wants to perform a hypothesis test to determine whether the quality of items produced appears to be independent of the production process used. What is the rejection point condition?

In performing a chi-square test of independence, as the differences between respective observed and expected frequencies ________, the probability of concluding that the row variable is independent of the column variable increases.

A U.S.-based company offers an online proficiency course in basic accounting. Completing this online course satisfies the Fundamentals of Accounting course requirement in many MBA programs. In the first semester, 315 students have enrolled in the course. The marketing research manager divided the country into seven regions of approximately equal population. The course enrollment values for each of the seven regions are given below. The management wants to know if there is equal interest in the course across all regions. At a significance level of .01, test H₀: the probabilities are equal for all seven regions.

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 What are the degrees of freedom for the chi-square test?

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. Calculate the value of the chi-square statistic.

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, what is the appropriate rejection point condition?

A survey was conducted on the age and gender of the purchasers of a specific automotive model. The results are below. Test the null hypothesis that age is independent of gender at α = .05.

A U.S.-based company offers an online proficiency course in basic accounting. Completing this online course satisfies the Fundamentals of Accounting course requirement in many MBA programs. In the first semester, 315 students have enrolled in the course. The marketing research manager divided the country into seven regions of approximately equal population. The course enrollment values for each of the seven regions are given below. The management wants to know if there is equal interest in the course across all regions. How many degrees of freedom are associated with the chi-square test? Also, at α = 0.05, determine the rejection point condition of the chi-square statistic.

A U.S.-based company offers an online proficiency course in basic accounting. Completing this online course satisfies the Fundamentals of Accounting course requirement in many MBA programs. In the first semester, 315 students have enrolled in the course. The marketing research manager divided the country into seven regions of approximately equal population. The course enrollment values for each of the seven regions are given below. The management wants to know if there is equal interest in the course across all regions. Calculate the expected enrollment (frequency) for all 7 regions.

While a binomial distribution describes count data that can be classified into one of two mutually exclusive categories, a ________ distribution describes count data that are classified into more than two mutually exclusive categories.