Exam 14: Analysis of Categorical Data

Which statistical technique is appropriate when we describe a single population of qualitative data with two or more categories?

Medical statistics show that deaths due to four major diseases:call them A, B, C, and D:account for 15%, 21%, 18%, and 14%, respectively, of all non-accidental deaths. A study of the causes of 616 non-accidental deaths at a hospital gives the following counts: Do these data provide sufficient evidence to indicate that the proportions of people dying of diseases A, B, C, and D at this hospital differ from the proportions accumulated for the population at large? Find the approximate p-value and use it to make your decision.

Numbers in a contingency table show the frequency of occurrence of all possible combinations of categories.

Which of the following must be known in order to determine the critical values in the chi-square distribution table?

Upon which of the following types of variables is the chi-square test of a contingency table based?

Business Decision Narrative The owner of Fit Forever Health Club is considering adding an indoor swimming pool to his facility. The manager decided to take a survey to determine whether member opinion about the addition of a pool was independent of the age of the member. Two hundred members were selected at random and asked to state their opinion. The following data were recorded: Opinion Concerning Pool Use the following output generated by statistical software to answer the questions below. Chi-Square Test Expected counts are printed below observed counts Chi-Sq = 2.482 + 0.604 + 1.091 + 0.000 + 0.197 + 0.204 + 4.119 + 0.193 +3.672 = 12.562 DF = 4, P-Value = 0.014 -Refer to Business Decision Narrative. What is the p-value associated with the test?

When the expected cell frequencies are smaller than five, the cells should be combined in a meaningful way such that the expected cell frequencies exceed five.

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. If you were to test this hypothesis using the chi-square statistic, how many degrees of freedom would the test have? What is the rejection region?

In 2003, the student body of a large university in Ontario consisted of 30% first-year students, 25% second-year students, 27% third-year students, and 18% graduate students. A sample of 400 students taken from the 2004 student body showed that there were 138 first-year students, 88 second-year students, 94 third-year students, and 80 graduate students. Test with 5% significance level to determine whether the student body proportions changed.

If there are more than two row categories in a contingency table with fixed c column totals, then the test of independence is equivalent to a test of the equality of c sets of multinomial proportions.

An experiment was conducted to investigate the effect of general hospital experience on the attitudes of physicians toward the lower-income group. A random sample of 50 physicians who had just completed 4 weeks of service in a general hospital were categorized according to their concern for lower-income group before and after their general hospital experience. The data are shown in the table. Do the data provide sufficient evidence to indicate a change in "concern" after the general hospital experience? If so, describe the nature of the change.

Business Decision Narrative The owner of Fit Forever Health Club is considering adding an indoor swimming pool to his facility. The manager decided to take a survey to determine whether member opinion about the addition of a pool was independent of the age of the member. Two hundred members were selected at random and asked to state their opinion. The following data were recorded: Opinion Concerning Pool Use the following output generated by statistical software to answer the questions below. Chi-Square Test Expected counts are printed below observed counts Chi-Sq = 2.482 + 0.604 + 1.091 + 0.000 + 0.197 + 0.204 + 4.119 + 0.193 +3.672 = 12.562 DF = 4, P-Value = 0.014 -Refer to Business Decision Narrative. What is the appropriate conclusion at the 0.05 level of significance? Justify your answer.

Tests of homogeneity are used to compare several binomial populations.

The degrees of freedom associated with a goodness-of-fit test equal the number of rows times the number of columns in the table.

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. State the null and alternative hypotheses.

When there are only two categories in a multinomial experiment, the experiment reduces to a binomial experiment.

Business Decision Narrative The owner of Fit Forever Health Club is considering adding an indoor swimming pool to his facility. The manager decided to take a survey to determine whether member opinion about the addition of a pool was independent of the age of the member. Two hundred members were selected at random and asked to state their opinion. The following data were recorded: Opinion Concerning Pool Use the following output generated by statistical software to answer the questions below. Chi-Square Test Expected counts are printed below observed counts Chi-Sq = 2.482 + 0.604 + 1.091 + 0.000 + 0.197 + 0.204 + 4.119 + 0.193 +3.672 = 12.562 DF = 4, P-Value = 0.014 -Refer to Business Decision Narrative. State the null and alternative hypotheses.

How many columns would the table associated with a contingency table test with 4 rows and 15 degrees of freedom have?

A statistics professor posted the following grade distribution guidelines for his elementary statistics class: 8% A, 35% B, 40% C, 12% D, and 5% F. A sample of 100 elementary statistics grades at the end of last semester showed 12 As, 30 Bs, 35 Cs, 15 Ds, and 8 Fs. Test at the 5% significance level to determine whether the actual grades deviate significantly from the posted grade distribution guidelines.

Which of the following is NOT a characteristic of a multinomial experiment?