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

We want to test whether type of car owned (domestic or foreign) is independent of gender. A contingence table is obtained from a sample of 990 people as At alpha = 0.05 level, we conclude that:

In a goodness-of-fit test about a population distribution, if one or more parameters are left unspecified in H0, they must be estimated from the sample data. This will reduce the degrees of freedom by ________ for each estimated parameter.

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 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.

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?

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.

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 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 test of independence, the difference expected value for the "40 and over and regularly use text messaging" cell is just over 43 people.

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 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. Based on the data above what is the expected value for the "under 21 and regularly use text messaging" cell?

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.

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.

In performing chi-square contingency analysis, to overcome a small expected cell frequency problem, we:

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 the test statistic for a chi-square goodness-of-fit test is larger than the critical value, the null hypothesis should be rejected.

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

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

When the variables of interest are both categorical and the decision maker is interested in determining whether a relationship exists between the two, a statistical technique known as contingency analysis is useful.

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

If the calculated chi-square statistic for specific degrees of freedom is a large value, this supports evidence that the fit of the actual data to the hypothesized distribution is not good, and HA should be rejected.