Exam 14: Categorical Data and Frequency Tables

A marketing research firm runs a well-designed survey to see if the color on the face of a golf club affects a golfer's preference.Golfers can choose one of three club face colors: gold (G), black (B), and tan (T).When 120 golfers are randomly sampled and asked to indicate their preference, 25 prefer the gold, 55 prefer the black, and 40 prefer the tan.The firm reports that it did a chi-square goodness-of-fit test on the data and decided there is enough statistical evidence, at = 0.01, to reject the idea that color does not matter to golfers.As the head of production for the golf club manufacturer that commissioned the study, you might:

Psychologists conduct a study to see if right-handed people have a greater tendency to turn right.In the study, 220 right-handed people are sent down an unfamiliar hallway that offers the possibility of turning left, turning right, or continuing straight.They are told that each direction will take them to the desired destination.It is postulated that right-handed people will turn right 75% of the time, turn left 5% of the time, and go straight 20% of the time.In the experiment, 165 of the people turn right, 11 turn left, and 44 go straight.Conduct a χ2 goodness-of-fit test to see if the data provide sufficient evidence to refute the postulated percentages.Select the appropriate critical value (CV), test statistic (TS), and decision.(Use α = 0.05.)

In a χ2 goodness-of-fit test, the decision to reject H₀ can be interpreted as:

A chi-square test for homogeneity can support a conclusion that:

In a goodness-of-fit test with 4 degrees of freedom, the chi-square test statistic is 10.25.Which of the following is true about the p-value?

A chi-square test for independence is appropriate for:

In a two-way frequency table, suppose one cell has a row total of 200 and a column total of 75, with a total sample size of 1000.What would that cell's expected count be?

A chi-square test for independence of two categorical variables is appropriate if:

In a χ2 test for homogeneity, the test statistic is 18.6732 and the critical value is 12.8325.What is the proper conclusion for the test?

In a test of homogeneity of proportions, if the null hypothesis is not rejected, then:

In a goodness-of-fit test, one sample showed that the observed frequency and the expected frequency eiwere quite different for each cell.We can conclude that:

A chi-square test of independence for a two-way frequency table with rows and columns results in a test statistic of 20.18.What can you conclude about the p-value for this test?

A chi-square test for homogeneity applies to:

In a χ2 goodness-of-fit test, is:

The distribution of class ranks in a particular introductory statistics class is assumed to be 20% freshmen, 40% sophomores, 35% juniors, and 5% seniors.To see if this is valid, a sample of 20 sections of this introductory statistics class is taken, and the frequency of each class rank is recorded.There are 130 freshmen, 242 sophomores, 221 juniors, and 37 seniors.The test statistic for a χ2goodness-of-fit test would be:

The target grade distribution for a particular course is 10% A, 30% B, 40% C, 15% D, 5% F.Students complain that a particular professor who teaches this course grades "too hard." The present students survey 250 former students of this professor's class and then do a χ2 goodness-of-fit test to see if the data provide sufficient evidence to support their complaint.They find a critical value of 14.7 and a test statistic of 9.8, with α = 0.10.What is the take-away conclusion from this survey?

A two-way frequency table:

In a chi-square goodness-of-fit test, what does the following mathematical statement yield? where . ​

In a chi-square test for homogeneity, the variables under consideration are:

If two categorical observations are made on the same individual or object, the data set is said to be: