Inference for Catergorial Data Multiple Choice Practice Problems for AP Statistics

Review the following concepts if necessary:

• Chi-Square Goodness-of-Fit Test for AP Statistics
• Two-Way Tables (Contingency Tables) Defined for AP Statistics
• Chi-square Test for Independence for AP Statistics
• Chi-Square Test for Homogeneity of Proportions (or Homogeneity of Populations) for AP Statistics

Problems

1. Find the expected value of the cell marked with the "***" in the following 3 × 2 table (the bold face values are the marginal totals):



1. 74.60
2. 18.12
3. 12.88
4. 19.65
5. 18.70
2. A Χ² goodness-of-fit test is performed on a random sample of 360 individuals to see if the number of birthdays each month is proportional to the number of days in the month. X² is determined to be 23.5. The P-value for this test is
   1. 0.001 < P < 0.005
   2. 0.02 < P < 0.025
   3. 0.025 < P < 0.05
   4. 0.01 < P < 0.02
   5. 0.05 < P < 0.10
3. Two random samples, one of high school teachers and one of college teachers, are selected and each sample is asked about their job satisfaction. Which of the following are appropriate null and alternative hypotheses for this situation?
   1. H₀: The proportion of each level of job satisfaction is the same for high school teachers and college teachers.

   H_A: The proportions of teachers highly satisfied with their jobs is higher for college teachers.

   2. H₀: Teaching level and job satisfaction are independent.

   H_A: Teaching level and job satisfaction are not independent.

   3. H₀: Teaching level and job satisfaction are related.

   H_A: Teaching level and job satisfaction are not related.

   4. H₀: The proportion of each level of job satisfaction is the same for high school teachers and college teachers.

   H_A: Not all of the proportions of each level of job satisfaction are the same for high school teachers and college teachers.

   5. H₀: Teaching level and job satisfaction are independent.

   H_A: Teaching level and job satisfaction are not related.

4. A group separated into men and women are asked their preference toward certain types of television shows. The following table gives the results.



Which of the following statements is (are) true?

1. The variables gender and program preference are independent.
2. For these data, X² = 0.
3. The variables gender and program preference are related.
1. I only
2. I and II only
3. II only
4. III only
5. II and III only
5. For the following two-way table, compute the value of X².



1. 2.63
2. 1.22
3. 1.89
4. 2.04
5. 1.45
6. The main difference between a Χ² test for independence and a Χ² test for homogeneity of proportions is which of the following?
   1. They are based on a different number of degrees of freedom.
   2. One of the tests is for a two-sided alternative and the other is for a one-sided alternative.
   3. In one case, two variables are compared within a single population. In the other case, two populations are compared in terms of a single variable.
   4. For a given value of X², they have different P-values.
   5. There are no differences between the tests. They measure exactly the same thing.
7. A study is to be conducted to help determine if ethnicity is related to blood type. Ethnic groups are identified as White, African-American, Asian, Latino, or Other. Blood types are A, B, O, and AB. How many degrees of freedom are there for a chisquare test of independence between Ethnicity and Blood Type?
   1. 5 × 4 = 20
   2. 5 × 3 = 15
   3. 4 × 4 = 16
   4. 5 + 4 – 2 = 7
   5. 4 × 3 = 12
8. Which of the following statements is (are) correct?
   1. A condition for using a Χ² test is that most expected values must be at least 5 and that all must be at least 1.
   2. A Χ² test for goodness of fit tests the degree to which a categorical variable has a specific distribution.
   3. Expected cell counts are computed in the same way for goodness of fit tests and tests of independence.
   1. I only
   2. II only
   3. I and II only
   4. II and III only
   5. I, II and III