Ch8 Test Bank + Hypothesis Testing With Categorical Data Chi

Chapter 8: Hypothesis Testing with Categorical Data: Chi Square

1. Let’s assume that you want to examine the relationship between the number of times a person has been bullied in his/her entire life and his/her level of self-esteem (low, moderate, high). You are not quite sure which statistical test of significance you want to use but decide to go with a chi square test of independence because the formulas are more understandable to you.
   1. Identify the IV and indicate the level of measurement.
   2. Identify the DV and indicate the level of measurement.
   3. Reflect on your decision and state whether the test you chose has been the most appropriate one to use. Also, explain your decision.
2. You’ve learned in your criminology class that low self-control is, according to Gottfredson and Hirschi (1990), a strong predictor for criminal behavior. You have administered a survey with a random sample of 350 high school students determining their level of self-control and you have categorized your findings into low self-control and high self-control. You also asked the participants whether they have ever been in contact with the criminal justice system (yes/no). Now you want to learn whether there is indeed a relationship between low self-control and criminal behavior. The results of your survey are presented in the table below. You set your alpha level at 0.05.
   1. Identify the independent and dependent variables and indicate the level of measurement for each variable.
   2. Compute the percentages for every cell.
   3. State your null hypothesis and your alternative hypotheses.
   4. Compute the degrees of freedom.
   5. State your decision rule.
   6. Compute expected frequencies for each cell.
   7. Compute chi square.
   8. Interpret your findings.

1. You want to determine whether gender has an impact on attitudes toward police. You conduct a survey with a random sample of 220 individuals over the age of 18 asking your participants about their attitudes about police (positive/negative). The results are presented in the table below. You set your alpha level at 0.01.
   1. Identify the independent and dependent variables and indicate the level of measurement for each variable.
   2. Compute the percentages for every cell.
   3. State your null hypothesis and your alternative hypotheses.
   4. Compute the degrees of freedom.
   5. State your decision rule
   6. Compute expected frequencies for each cell.
   7. Compute chi square.
   8. Interpret your findings.

1. Now that you know about the attitudes of females and males toward police, you want to find whether there is also a relationship between gender (female/male) and official complaints filed (yes/no) after a citizen–police encounter. You send a follow-up survey to the participants already interviewed and 198 of 220 agree to answer the question of whether they have ever filed an official complaint after a citizen–police encounter (yes/no). The results are listed in the table below. This time you select an alpha level of 0.05.
   1. Identify the independent and dependent variables and indicate the level of measurement for each variable.
   2. Compute the percentages for every cell.
   3. State your null hypothesis and your alternative hypothesis.
   4. Compute the degrees of freedom.
   5. State your decision rule.
   6. Compute expected frequencies for each cell.
   7. Compute chi square.
   8. Interpret your findings.

1. Prostitution is illegal in all states of the United States (except in some counties in Nevada). You are interested to find whether there is a relationship between gender (male/female/transgender) and attitudes regarding the legal status of prostitution (legalize/decriminalize/criminalize). You draw a random sample of 450 individuals over the age of 18 who are residents of Texas. The results of your survey are presented below. You set an alpha level of 0.05.
   1. Identify the independent and dependent variables and indicate the level of measurement.
   2. Compute the percentages for every cell.
   3. State your null hypothesis and your alternative hypothesis.
   4. Compute the degrees of freedom.
   5. State your decision rule.
   6. Compute expected frequencies for each cell.
   7. Compute chi square.
   8. Interpret your findings.

1. You rejected the null hypothesis for the following cases (2 × 2 tables) and thus found a real difference between the sample means. However, you want to know how strong the relationship is.
   1. Determine which test of association is appropriate for a chi square with two variables with two categories.
   2. Compute the strength of the relationship for the following and interpret your results.
      1. χ² = 4.235; n = 153
      2. χ² = 18.567; n = 215
      3. χ² = 3.898; n = 310
      4. χ² = 22.33; n = 146
      5. χ² = 10.659; n = 189
      6. χ² = 29.66; n = 195
2. You calculated chi square for several cases that have a table greater than 2 × 2. To determine the strength of the relationship, calculate Cramer’s V and interpret your results.
   1. χ² = 39.56; n = 166; 3 rows and 3 columns
   2. χ² = 22.15; n = 123; 2 rows and 3 columns
   3. χ² = 15.26; n = 213; 4 rows and 3 columns
   4. χ² = 44.13; n = 286; 3 rows and 5 columns
   5. χ² = 10.22; n = 145; 3 rows and 4 columns
   6. χ² = 29.36; n = 226; 6 rows and 5 columns