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

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

In a goodness-of-fit test,when the null hypothesis is true,the expected value for the chi-square test statistic is zero.

In a chi-square contingency analysis,when expected cell frequencies drop below 5,the calculated chi-square value tends to be inflated and may inflate the true probability of ________ beyond the stated significance level.

A lube and oil change business believes that the number of cars that arrive for service is the same each day of the week.If the business is open six days a week (Monday - Saturday)and a random sample of n = 200 customers is selected,the expected number that will arrive on Monday is about 33.33.

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 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 expected number of people in the sample who bought a German made car and who lived on the East Coast is just under 40 people.

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 the expected number of days on which exactly 1 machine breaks down is 40.96.

Contingency analysis helps to make decisions when multiple proportions are involved.

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.

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 hypothesis test is to be conducted using a .05 level of significance,which of the following is correct critical value?

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:

If any of the observed frequencies are smaller than 5,then categories should be combined until all observed frequencies are at least 5.

In testing a hypothesis that two categorical variables are independent using the x² test,the expected cell frequencies are based on assuming:

A lube and oil change business believes that the number of cars that arrive for service is the same each day of the week.If the business is open six days a week (Monday - Saturday)and a random sample of n = 200 customers is selected,the critical value for testing the hypothesis using a goodness-of-fit test is x₂ = 9.2363 if the alpha level for the test is set at .10.

The Bradfield Container Company makes "cardboard" boxes for commercial use (i.e. ,pizza boxes).One of the big issues for the company is the set-up time required to change over from one order to the next.At one particular machine,the set-up time is thought to be uniformly distributed between 10 and 21 minutes.To test whether this is true or not,a random sample of 180 set-ups on this machine was selected with set-up time rounded to the nearest two-minute intervals.The following results occurred: Set-up Time Frequency 10-11 minutes 13 12-13 minutes 23 14-15 minutes 40 16-17 minutes 44 18-19 minutes 40 20-21 minutes 20 a.What are the appropriate null and alternative hypothesis to be tested? b.Based on the null and alternative hypotheses stated in part a,determine the expected frequencies for each set-up time category. c.Assuming that we wish to conduct the hypothesis test at the .05 level,what is the critical value that should be used? d.Compute the test statistic and carry out the hypothesis test.

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:

Consider a goodness-of-fit test with a computed value of chi-square = 1.273 and a critical value = 13.388,the appropriate conclusion would be 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 contingency analysis using a 0.01 level of significance,the value of the critical value is:

Contingency analysis is used only for numerical data.

We expect the actual frequencies in each cell to approximately match the corresponding expected cell frequencies when: