Exam 14: Analysis of Categorical Data

In a chi-square test of independence, the value of the test statistic was , and the critical value at was 11.1433. Which of the following conclusions may we draw from this information?

How is a chi-square goodness-of-fit test conducted?

Consider a cell in a contingency table. Given the cell's row total of 200, the cell's column total of 75, and a sample size of 1000, what is the cell's expected frequency?

Ice Cream Flavours Narrative The four most popular flavours of a particular brand of ice cream are French vanilla, natural vanilla, chocolate chip, and caramel almond swirl. The question arose as to whether each of these flavours is equally preferred. To answer that question, a random sample of 160 sales was selected, yielding the following data: -Refer to Ice Cream Flavours Narrative. Set up the appropriate rejection region for $\alpha$ = 0.10.

The large-sample z tests for one and two binomial proportions are special cases of the chi-square statistic.

The data that result from two binomial experiments can be displayed as a two-way classification with two rows and two columns, so that the chi-square test of homogeneity can be used to compare the two binomial proportions and .

In chi-square tests, there is a rule known as Rule of Five. What does this rule require?

Suppose that a response can fall into one of k = 5 categories with probabilities , and that n = 250 responses produced these category counts: The categories represent five car salespersons, and the observed frequencies represent the number of cars sold in a six-month period. -Refer to Car Sales Narrative. Calculate the observed value of the test statistic.

The middle 0.95 portion of the chi-square distribution with 9 degrees of freedom has table values of 3.32511 and 16.9190, respectively.

The goodness-of-fit test is a two-way classification with cell probabilities specified in .

To be valid, a chi-square test of independence requires that each expected frequency equal 30 or more.

Average Casino Dice Rolls Narrative A casino customer is concerned about whether the dice the casino is using are "fair" (i.e., each face is equally likely to appear). The customer obtains a die that is being used by the casino and rolls it 240 times. The customer records the following data: -Refer to Average Casino Dice Rolls Narrative. Set up the appropriate rejection region for = 0.10.

Upon which of the following kinds of variables is the chi-square test of independence based?

Ages of National College Students Narrative A national survey states that 67% of college students are under the age of 25, 21% are between the ages of 25 and 30, 8% are between 30 and 40, and 4% are over 40. A random sample of 250 students at Vanier College in Montreal yielded the following data: -A sample survey of 850 people in Calgary was conducted in 2001 to see how people get to work. The results are shown in the frequency table below. A study of the same nature was conducted in 1990 and revealed 12% walk, 67% drive an automobile, 18% take a bus, and 3% ride a bicycle. Do the current data support that the proportions are the same as in 1990? Use $\alpha$ = 0.025.

A sport preference poll showed the following data for men and women: Use the 5% level of significance and test to determine whether sport preferences depend on gender.

Is there a difference in the spending patterns of high-school seniors depending on their gender? A study to investigate this question focused on 196 employed high-school seniors. Students were asked to classify the amount of their earnings that they spent on their car during a given month: A portion of the computer printout is given here. Use the printout to analyze the relationship between spending patterns and gender. Write a short paragraph explaining your statistical conclusions and their practical implications. Chi-Sq = 0.985 + 0.167 + 0.735 + 0.962 + 0.500 + 0.985 + 0.167 + 0.735 + 0.962 + 0.500 = 6.696 DF = 4, P-Value = 0.153 2 cells with expected counts less than 5.0

A chi-square goodness-of-fit test with 3 degrees of freedom results in a test statistic of 6.789. Using the chi-square table, the most accurate statement that can be made about the p-value for this test is that 0.05 < p-value < 0.10.

A large carpet store wishes to determine if the brand of carpet purchased is related to the purchaser's family income. As a sampling frame, the store mailed a survey to people who have a store credit card. Five hundred customers returned the survey and the results follow: At the 5% level of significance, can you conclude that the brand of carpet purchased is related to the purchaser's family income? Justify your answer.

Seat Belts On School Buses Narrative A study was conducted to determine whether opinion concerning the addition of seat belts in school buses is independent of the population density in which a person resides. The following data were recorded: Local Use the following output generated using statistical software to answer the questions below. Chi-Square Test Expected counts are printed below observed counts Chi-Sq = 0.003 + 0.402 + 0.393 + 0.099 + 0.000 + 0.101 + 0.152 + 2.016 + 0.837 = 4.003 DF = 4, P-Value = 0.406 -Refer to Seat Belts On School Buses Narrative. What is the value of the test statistic?

A sports enthusiast believes that among sports television viewers 60% prefer to watch hockey, 25% prefer basketball, and 15% prefer football. A random sample of 120 viewers was selected and the following data recorded: Perform the appropriate test of hypothesis to determine whether the percentages are correct. Use $\alpha$ = 0.05.