Exam 13: Chi-Square Tests

The AAA Co. is interested in the level of satisfaction of their employees with the benefit package that they offer compared to their major competitors. A consultant hired to conduct the satisfaction survey told AAA Co. that the distribution of level of satisfaction at other companies is displayed below. A survey was conducted of 125 AAA employees with the following results. What are the expected values of the number of AAA employees at each satisfaction level, assuming a similar distribution as the major competitors of AAA?

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

The AAA Co. is interested in the level of satisfaction of their employees in the benefit package that they offer compared to their major competitors. A consultant hired to conduct the satisfaction survey told AAA Co. that the distribution of level of satisfaction at other companies is displayed below. A survey was conducted of 125 AAA employees with the following results. Using the critical value for α = .05, test the null hypothesis that the distribution of AAA employees at each satisfaction level is similar to the distribution of the employees of their major competitors.

A study of car accidents and drivers who use cell phones collects the following sample data. Calculate the chi-square statistic for this test of independence.

The chi-square goodness-of-fit test will be valid if the average of all of the expected cell frequencies is ________.

Which, if any, of the following statements about the chi-square test of independence is false?

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 freshmen who drop out of 2-year institutions that will be used in the chi-square test of independence.

On the most recent tax cut proposal, a random sample of Democrats and Republicans in the Congress cast their votes as follows. At a significance level of .01, determine the appropriate degrees of freedom and the rejection point condition for this test.

A study of car accidents and drivers who use cell phones collects the following sample data. Use a significance level of .05 and determine if cell phone use and accidents are independent. Null hypothesis is that accidents are independent of cell phone use.

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. Calculate the expected number of defective units produced by Process 1.

The AAA Co. is interested in the level of satisfaction of their employees with the benefit package that they offer compared to their major competitors. A consultant hired to conduct the satisfaction survey told AAA Co. that the distribution of level of satisfaction at other companies is displayed below. A survey of 125 AAA employees gave the following results. What are the degrees of freedom for testing the goodness of fit at α = .05?

When we carry out a chi-square test of independence, the expected frequencies are based on the null hypothesis.

When using a chi-square goodness-of-fit test with multinomial probabilities, the rejection of the null hypothesis indicates that at least one of the multinomial probabilities is not equal to the value stated in the null hypothesis.

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

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. Test the hypothesis that the original population is a normal distribution at .05.

The χ² statistic is used to test whether the assumption of normality is reasonable for a given population distribution. The sample consists of 5,000 observations and is divided into 6 categories (intervals). The degrees of freedom for the chi-square statistic are

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 60 - 79.99.

In the past, of all the students enrolled in Basic Business Statistics, 10 percent earned an A, 20 percent earned a B, 30 percent earned a C, 20 percent earned a D, and the remainder failed the course. Dr. Johnson is a new professor teaching Basic Business Statistics for the first time this semester. At the conclusion of the semester, of his 60 students, 10 had earned an A, 20 a B, 20 a C, 5 a D, and 5 received an F. Assume that the class constitutes a random sample. Dr. Johnson wants to know if there is sufficient evidence to conclude that the grade distribution of his class is different from the historical grade distribution. At α = .05, test to determine if the grade distribution for this class is different from the historical grade distribution.

The trials of a multinomial probability are assumed to be dependent.

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. What is the df for this chi-square test of normality?