Exam 14: Analysis of Categorical Data

The rejection region of the chi-square goodness-of-fit test is , where k is the number of categories and is the value of the test statistics.

The president of a large university collected data from students concerning building a new library, and classified the responses into different categories (strongly agree, agree, undecided, disagree, strongly disagree) and according to whether the student was male or female. To determine whether the data provide sufficient evidence to indicate that the responses depend upon gender, which of the following would be the most appropriate test?

In which of the following situations are contingency tables used?

In the chi-square goodness-of-fit test, if the expected frequencies, , and the observed frequencies, , were very different, what would we conclude?

To determine whether a single coin is fair, the coin was tossed 250 times, and heads was observed 140 times. What is the value of the test statistic?

Which of the following is the number of degrees of freedom for a contingency table with six rows and six columns?

Suppose you wish to test the null hypothesis that three binomial parameters , , and are equal versus the alternative hypothesis that at least two of the parameters differ. Independent random samples of 100 observations were selected from each of the populations. The data are shown in the table: a. Write the null and alternative hypotheses for testing the equality of the three binomial proportions. b. Calculate the test statistic and find the approximate p-value for the test in the previous question. c. Use the approximate p-value to determine the statistical significance of your results. If the results are statistically significant, explore the nature of the differences in the three binomial proportions.

In 2003, Brand A microwaves had 45% of the market, Brand B had 35%, and Brand C had 20%. This year the makers of Brand C launched a heavy advertising campaign. A random sample of appliance stores shows that, of 10,000 microwaves sold, 4,350 were Brand A, 3,450 were Brand B, and 2,200 were Brand C. Has the market changed? Test at 0.01.

A chi-square test for independence is applied to a contingency table with four rows and four columns for two qualitative variables. The degrees of freedom for this test must be 9.

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. What is the appropriate conclusion?

Which of the following procedures would be considered a suitable application for the chi-square technique?

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: -Refer to Ages of National College Students Narrative. Compute the value of the test statistic.

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: -Refer to Ages of National College Students Narrative. State the null and alternative hypotheses to test whether the distribution of students' ages at Vanier College agrees with the national survey.

A study of the purchase decisions of three stock portfolio managers, A, B, C, was conducted to compare the numbers of stock purchases that resulted in profits over a time period less than or equal to one year. One hundred randomly selected purchases were examined for each of the managers. Do the data provide evidence of differences among the rates of successful purchases for the three managers?

The chi-square goodness-of-fit test involves two categorical variables.

Whenever the expected frequency of a cell is less than five, one remedy for this condition is to increase the significance level.

A market research study was conducted to compare three different brands of car oil. The results of the study are summarized below. Use the accompanying statistical software output and = 0.005 to determine whether the brand of oil is independent of opinion. Chi-Square Test Expected counts are printed below observed counts Chi-Sq = 11.015 + 0.091 + 12.878 + 3.295 + 0.048 + 2.336 + 4.429 + 0.773 + 9.326 = 44.192 DF = 4, P-Value = 0.000

A chi-square test of independence with 10 degrees of freedom results in a test statistic of 19.25. Using the chi-square table, which of the following is the most accurate statement that can be made about the p-value for this test?