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

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 sum of the expected cell frequencies will equal 1,240.

It is believed that the number of drivers who are ticketed for speeding on a particular stretch of highway is a Poisson distribution with a mean of 3.5 per hour.A random sample of 100 hours is selected with the following results: Given this information,and without regard to whether there is a need to combine cells due to expected cell frequencies,the critical value for testing whether the distribution is Poisson with a mean of 3.5 per hour at an alpha level of .05 is x² = 15.5073.

If a contingency analysis test is performed with a 4 × 6 design,and if alpha = .05,the critical value from the chi-square distribution is 24.9958

In order to apply the chi-square contingency methodology for quantitative variables,we must first break the quantitative variable down into discrete categories.

The degrees of freedom for the chi-square goodness-of-fit test are equal to ________,where k is the number of categories.

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:

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,the sample size used in this study was nine.

If a sample with n = 60 subjects distributed over 3 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?

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

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 with an alpha equal to .05,the critical value will be a chi-square value with 9 degrees of freedom.

In conducting a test of independence for a contingency table that has 4 rows and 3 columns,the number of degrees of freedom is 11.

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. What is the value of the test statistic needed to conduct a goodness-of-fit test?

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,which of the following conclusions should be reached if the appropriate hypothesis is conducted using an alpha = .05 level?

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 study was recently conducted in which people were asked to indicate which new 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 expected frequency in the cell,radio-under 21 cell is 30.

If a contingency analysis test performed with a 4 × 6 design results in a test statistic value of 18.72,and if alpha = .05,the null hypothesis that the row and column variable are independent should be rejected.

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 of the following values is the correct value of the test statistic?

The reason that a decision maker might want to combine groups before performing a goodness-of-fit test is to avoid accepting the null hypothesis due to an inflated value of the test statistic.

Contingency analysis can be used when the level of data measurement is nominal or ordinal.

Explain the basic logic behind the chi-square goodness-of-fit test.