Exam 12: Experimental Design and Analysis of Variance

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.

In a contingency table,when all the expected frequencies equal the observed frequencies,the calculated χ² statistic equals zero.

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.

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 contingency table summarizes data that has been classified on 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.

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 correct.

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.

A study of car accidents and drivers who use cell phones collects the following sample data. At a significance level of 0.05,determine the appropriate degrees of freedom and the rejection point condition for the test.

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

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)?

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.

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.

When we carry out a chi-square test of independence,if r_i is the row total for row i and c_j is the column total for column j,then the estimated expected cell frequency corresponding to row i and column j equals (r_i)(c_j)/n.

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. What is the appropriate null hypothesis?

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.Very Satisfied 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 goodness-of-fit chi-square test,the expected frequencies are based on the alternative hypothesis.

As the difference between observed frequency and expected frequency _______________,the probability of rejecting the null hypothesis increases.

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. Use a significance level of .05 and determine if the type of school and the drop rate are independent.(Null hypothesis is that dropout rate is independent of type of school. )

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.