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

When the expected cell frequencies are smaller than 5,the cells should be combined in a meaningful way such that the expected cell frequencies do exceed 5.

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.

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

The sampling distribution for a goodness-of-fit test is the Poisson distribution.

In a chi-square contingency analysis application,the expected cell frequencies will be equal in all cells if the null hypothesis is true.

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.

What does the term observed cell frequencies refer to?

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.

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.

Recently a survey was conducted involving customers of a fitness center in Dallas,Texas.Participants were asked to indicate how often they use the club by checking one of the following categories: 0-1 time per week;2-3 times per week;4-5 times per week;more than 5 times.The following data show how males and females responded to this question. One of the purposes of the survey was to determine whether there is a relationship between the gender of the customer and the number of visits made each week. a.State the appropriate null and alternative hypothesis. b.What test procedure is appropriate to use to conduct this test? c.Conduct the hypothesis test using an alpha = .05 level.

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 number of degrees of freedom is:

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?

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

Unlike the case of goodness-of-fit testing,with contingency analysis there is no restriction on the minimum size for an expected cell frequency.

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.

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 the sample size is large,the standard normal distribution can be used in place of the chi-square in a goodness-of-fit test for testing whether the population is normally distributed.

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 the expected values are based on the assumption that the two variables are independent of each other.

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.