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

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.

A goodness-of-fit test can be used to determine whether a set of sample data comes from a specific hypothesized population distribution.

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 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 sum of the expected cell frequencies will be equal to the sum of the observed cell frequencies.

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

If the null hypothesis is not rejected,you do not need to worry when the expected cell frequencies drop below 5.0.

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.

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 chi-square test for goodness-of-fit is used to test whether or not there are any preferences among 3 brands of peas.If the study uses a sample of n = 60 subjects,then the expected frequency for each category would be:

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?

In testing a hypothesis that two categorical variables are independent using the test,the expected cell frequencies are based on assuming:

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.

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.

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 critical value from the chi-square table is based on 8 degrees of freedom.

In a chi-square contingency test,the number of degrees of freedom is equal to the number of cells minus 1.

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,if the appropriate null hypothesis is tested using a significance level equal to .05,which of the following conclusions should be reached?

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.

In a chi-square goodness-of-fit test,by combining cells we guard against having an inflated test statistic that could have caused us to:

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.