Exam 13: Chi-Square Tests

A study of car accidents and drivers who use cell phones collects the following sample data. At a significance level of .05, determine the appropriate degrees of freedom and the rejection point condition for the test.

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 40 − 59.99.

Consider the 3 × 2 contingency table below. At a significance level of .05, test H₀: the factors A and B are independent.

On the most recent tax cut proposal, a random sample of Democrats and Republicans in the Congress cast their votes as follows. Calculate the chi-square statistic for this test of independence.

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 row total, calculate the corresponding percentage.

Expected cell frequencies for a multinomial distribution are calculated by assuming statistical dependence.

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 What is the expected value of the number of billings for each center if H₀ (equal probabilities) is true?

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 What is the critical value at α = .01 to test the null hypothesis (equal billings from each center)?

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. Use α = .05 and determine the appropriate degrees of freedom and the rejection point condition associated with this goodness-of-fit test.

When we carry out a chi-square test of independence, as the differences between the respective observed and expected frequencies decrease, the probability of concluding that the row variable is independent of the column variable

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. Assume that H₀: p₁ = p₂ = p₃ = p₄ = p₅ = p₆ = p₇ is not rejected, and state a one-sentence managerial conclusion.

A multinomial probability distribution describes data that are classified into two or more categories when a multinomial experiment is carried out.

Consider the 3 × 2 contingency table below. Compute the expected frequencies in row 1.

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 probability for each interval, assuming a normal distribution.

When we carry out a chi-square test of independence, the alternate hypothesis states that the two relevant classifications

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 chi-square test statistic for testing the hypothesis that the original population is a normal distribution?

The χ² statistic from a contingency table with 6 rows and 5 columns will have

The χ² goodness-of-fit test requires the nominative level of data.

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. Test the null hypothesis that score is independent of education level at α = .01.

A fastener manufacturing company uses a chi-square goodness-of-fit test to determine if a population of all lengths of ¼-inch bolts it manufactures is distributed according to a normal distribution. If we reject the null hypothesis, it is reasonable to assume that the population distribution is approximately normally distributed.