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

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,which test would be used to properly analyze the data in this experiment?

Explain why,in performing a goodness-of-fit test,it is sometimes necessary to combine categories.

By combining cells we guard against having an inflated test statistic that could have led us to incorrectly reject the H₀.

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

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. Based on these data,conduct a goodness-of-fit test using a 0.10 level of significance.Which conclusion is correct?

A survey was recently conducted in which males and females were asked whether they owned a laptop personal computer.The following data were observed: Given this information,if an alpha level of .05 is used,the test statistic for determining whether having a laptop is independent of gender is approximately 14.23.

Which of the following statements is true in the context of a chi-square goodness-of-fit test?

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,assuming that all expected values are sufficiently large to use the classes as shown above,the critical value based on a 0.05 level of significance is 9.4877.

In a contingency analysis,we expect the actual frequencies in each cell to approximately match the corresponding expected cell frequencies when H₀ is true.

Managers use contingency analysis to determine whether two categorical variables are independent of each other.

A survey was recently conducted in which males and females were asked whether they owned a laptop personal computer.The following data were observed: Given this information,if an alpha level of .05 is used,the sum of the expected cell frequencies will be equal to the sum of the observed cell frequencies.

A lube and oil change business believes that the number of cars that arrive for service is the same each day of the week.If the business is open six days a week (Monday - Saturday)and a random sample of n = 200 customers is selected,the sum of the expected frequencies over the six days cannot be determined without seeing the actual sample data.

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,the cell with the largest expected cell frequency is also the cell with the largest observed frequency.

A goodness-of-fit test can be used to determine whether a set of sample data comes from a specific hypothesized population distribution.

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 survey was recently conducted in which males and females were asked whether they owned a laptop personal computer.The following data were observed: Given this information,the sample size in the survey was 300 people.

How can the degrees of freedom be found in a contingency table with cross-classified data?

A study was recently done in the United States in which car owners were asked to indicate whether their most recent car purchase was a U.S.car,a German car,or a Japanese car.The people in the survey were divided by geographic region in the United States.The following data were recorded. Given this situation,to test whether the car origin is independent of the geographical location of the buyer,the critical value for alpha = .10 is 14.6837.

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 9.4877.

A study published in the American Journal of Public Health was conducted to determine whether the use of seat belts in motor vehicles depends on ethnic status in San Diego County.A sample of 792 children treated for injuries sustained from motor vehicle accidents was obtained,and each child was classified according to (1)ethnic status (Hispanic or non-Hispanic)and (2)seat belt usage (worn or not worn)during the accident.The number of children in each category is given in the table below. Referring to these data,the calculated test statistic is: