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

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?

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. The degrees of freedom for the test will be 7.

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:

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.

The logic behind the chi-square goodness-of-fit test is based on determining how far the actual observed frequencies are from the expected frequencies.

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 a contingency analysis, the greater the difference between the actual and the expected frequencies, the more likely:

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 goodness-of-fit test is always a one-tail test with the rejection region in the lower tail.

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.

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. Using this data, if we wish to test whether the preferred news source is independent of age using a 0.05 level of significance, the critical value is 5.9915.

In a chi-square contingency analysis application, the expected cell frequencies will be equal in all cells if the null hypothesis 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, for an alpha = .05 level, the test statistic is computed to be approximately 40.70.

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 for testing the hypothesis will be based on 5 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.

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 follow data has been collected from a random sample of their customers. Using the data above, in order to test for the independence of age and the use of text messaging, the expected value for the "under 21 and regularly use text messaging" cell is 82.

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 null hypothesis to be tested is that the car origin is dependent on the geographical location of the buyer.

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

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