Exam 13: Chi-Square Tests

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 80 and higher.

A special version of the chi-square goodness-of-fit test that involves testing the null hypothesis that all of the multinomial probabilities are equal is called the test for ________.

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 conforming units produced by Process 2.

When we carry out a chi-square goodness-of-fit test for a normal distribution, the null hypothesis states that the population

On the most recent tax cut proposal, a random sample of Democrats and Republicans in the Congress cast their votes as follows. Suppose that the chi-square test of independence is performed and the null hypothesis (the vote on the issue and party affiliation are independent) is rejected. Provide a one-sentence interpretation of the outcome of the test.

Consider the 3 × 2 contingency table below. At α = .05, determine the tabular value of the chi-square statistic used to test for the independence of factors A and B.

In performing a chi-square goodness-of-fit test for a normal distribution, a researcher wants to make sure that all of the expected cell frequencies are at least five. The sample is divided into 7 intervals. The second through the sixth intervals all have expected cell frequencies of at least five. The first and the last intervals have expected cell frequencies of 1.5 each. After adjusting the number of intervals, the degrees of freedom for the chi-square statistic is ________.

As the difference between observed frequency and expected frequency ________, the probability of rejecting the null hypothesis 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. Assume that H₀, the probabilities are equal for all seven regions, is rejected. State a one-sentence managerial conclusion.

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. At a significance level of .05, determine the appropriate degrees of freedom and the rejection point condition for this 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 expected absences for all 5 days.

In performing a chi-square goodness-of-fit test for a normal distribution, if there are 7 intervals, then the number of degrees of freedom for the chi-square statistic is ________.

The chi-square goodness-of-fit test can only be used to test whether a population has specified multinomial probabilities or to test if a sample has been selected from a normally distributed population. It cannot be used if sample data come from other distribution forms, such as the Poisson.

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. Chi-Square Contingency Table Test for Independence At a significance level of 0.05, the management wants to perform a hypothesis test to determine if the quality of the items produced appears to be independent of the production process used. Based on the results summarized in the MegaStat/Excel output provided in the table above, we

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 to determine whether the quality of the items produced appears to be the same for all three processes. What is the null hypothesis?

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 value of the chi-square statistic.

In performing a chi-square goodness-of-fit test with multinomial probabilities, the smaller 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.

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. Calculate the chi-square statistic.

When using the chi-square goodness-of-fit test, if the value of the chi-square statistic is large enough, we reject the null hypothesis.

When we carry out a goodness-of-fit chi-square test, the expected frequencies are based on the alternative hypothesis.