Exam 13: Goodness-Of-Fit Tests and Contingency Analysis

The billing department of a national cable service company is conducting a study of how customers pay their monthly cable bills. The cable company accepts payment in one of four ways: in person at a local office, by mail, by credit card, or by electronic funds transfer from a bank account. The cable company randomly sampled 400 customers to determine if there is a relationship between the customer's age and the payment method used. The following sample results were obtained: Based on the sample data, can the cable company conclude that there is a relationship between the age of the customer and the payment method used? Conduct the appropriate test at the alpha= 0.01 level of significance.

A chi-square test for goodness-of-fit is used to test whether or not there are any preferences among 3 brands of peas. If the study uses a sample of n = 60 subjects, then the expected frequency for each category would be:

If a sample with n = 30 subjects distributed over 5 categories was selected, a chi-square test for goodness-of-fit will be used. How many degrees of freedom will be used in determining the chi-square test statistic?

When testing for independence in a contingency table with 3 rows and 4 columns, there are ________ degrees of freedom.

The Bradfield Container Company makes "cardboard" boxes for commercial use (i.e., pizza boxes). One of the big issues for the company is the set-up time required to change over from one order to the next. At one particular machine, the set-up time is thought to be uniformly distributed between 10 and 21 minutes. To test whether this is true or not, a random sample of 180 set-ups on this machine was selected with set-up time rounded to the nearest two-minute intervals. The following results occurred: a. What are the appropriate null and alternative hypothesis to be tested? b. Based on the null and alternative hypotheses stated in part a, determine the expected frequencies for each set-up time category. c. Assuming that we wish to conduct the hypothesis test at the .05 level, what is the critical value that should be used? d. Compute the test statistic and carry out the hypothesis test.

A walk-in medical clinic believes that arrivals are uniformly distributed over weekdays (Monday through Friday). It has collected the following data based on a random sample of 100 days. Assuming that a goodness-of-fit test is to be conducted using a 0.10 level of significance, the critical value is:

To employ contingency analysis, we set up a 2-dimensional table called a contingency table.

A business with 5 copy machines keeps track of how many copy machines need service on a given day. It believes this is binomially distributed with a probability of p = 0.2 of each machine needing service on any given day. It has collected the following based on a random sample of 100 days. Given this information the expected number of days on which exactly 1 machine breaks down is 40.96.

Many companies use well-known celebrities as spokespeople in their TV advertisements. A study was conducted to determine whether brand awareness of female TV viewers and the gender of the spokesperson are independent. Each in a sample of 300 female TV viewers was asked to identify a product advertised by a celebrity spokesperson. The gender of the spokesperson and whether or not the viewer could identify the product was recorded. The numbers in each category are given below. Referring to these sample data, if the appropriate null hypothesis is tested using a significance level equal to .05, which of the following conclusions should be reached?

To use contingency analysis for numerical data, which of the following is true?

If any of the observed frequencies are smaller than 5, then categories should be combined until all observed frequencies are at least 5.

A goodness-of-fit test can decide whether a set of data comes from a specific hypothesized distribution.

We expect the actual frequencies in each cell to approximately match the corresponding expected cell frequencies when:

For a chi-square test involving a contingency table, suppose H0 is rejected. We conclude that the two variables are:

The Conrad Real Estate Company recently conducted a statistical test to determine whether the number of days that homes are on the market prior to selling is normally distributed with a mean equal to 50 days and a standard deviation equal to 10 days. The sample of 200 homes was divided into 8 groups to form a grouped data frequency distribution. If a chi-square goodness-of-fit test is to be conducted using an alpha = .05, the critical value is 14.0671.

In testing a hypothesis that two categorical variables are independent using the x2 test, the expected cell frequencies are based on assuming:

A study was recently conducted in which people were asked to indicate which news medium was their preferred choice for national news. The following data were observed: Given this data, if we wish to test whether the preferred news source is independent of age, for an alpha = .05 level, the critical value from the chi-square table is based on 8 degrees of freedom.

A contingency table and a cross-tabulation table are two separate things and should not be used for the same purpose.

Many companies use well-known celebrities as spokespeople in their TV advertisements. A study was conducted to determine whether brand awareness of female TV viewers and the gender of the spokesperson are independent. Each in a sample of 300 female TV viewers was asked to identify a product advertised by a celebrity spokesperson. The gender of the spokesperson and whether or not the viewer could identify the product was recorded. The numbers in each category are given below. Referring to these sample data, if the appropriate hypothesis test is to be conducted using a .05 level of significance, which of the following is correct critical value?

In a chi-square contingency test, the number of degrees of freedom is equal to the number of cells minus 1.