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

A cell phone company wants to determine if the use of text messaging is independent of age.The following data has been collected from a random sample of customers. To conduct a contingency analysis using a 0.01 level of significance,the value of the critical value is:

If one or more parameters are left unspecified in a goodness-of-fit test,they must be estimated from the sample data and one degree of freedom is lost for each parameter that must be estimated.

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 = 15.5073.

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.

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. To conduct a goodness-of-fit test,what is the expected value for Friday?

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 having a laptop is independent of gender,the expected number of males with laptops in this survey is 150.

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?

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

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

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

A cell phone company wants to determine if the use of text messaging is independent of age.The following data has been collected from a random sample of customers. To conduct a contingency analysis,the value of the test statistic is:

A researcher is using a chi-square test to determine whether there are any preferences among 4 brands of orange juice.With alpha = 0.05 and n = 30,the critical region for the hypothesis test would have a boundary of:

If a contingency analysis test performed with a 4 x 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.

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.

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.

We are interested in determining whether the opinions of the individuals on gun control (as to Yes,No,and No Opinion)are uniformly distributed. A sample of 150 was taken and the following data were obtained. The conclusion of the test with alpha = 0.05 is that the views of people on gun control are

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?

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.

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

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