STATISTICS
Chapter 9: Testing Hypothesis with Categorical Data
1. Research suggests that individuals with childhood delinquency record are more likely to have adult criminality. You want to test this hypothesis with your sample data. The following table shows the association between childhood delinquency and adult criminality:
Not Criminal Criminal Total
Not Delinquent 14 6 20
Delinquent 8 22 30
Total 22 28 50
a) What are the independent and dependent variables in your study? How are they measured (nominal, ordinal, interval, ratio)?
Answer: IV:
DV:
b) Conduct a hypothesis with a .05 significance level to determine whether the relationship between delinquent status and criminal status is statistically significant. Be sure to identify the 5 steps of your hypothesis test and interpret your results accordingly.
Answer:
Step 1:
Step 2:
Step 3:
Step 4:
Cell Frequency Observed Frequency
Expected fo – fe (fo – fe) 2
A 14
B 6
C 8
D 22
Total =
Step 5:
c) Calculate the phi coefficient (F). What does this tell you?
Answer: F = =
2. A recent study found that individuals with military experience are more likely to have been incarcerated for a violent offense. You want to know if military experience also causes individuals to be more likely to be incarcerated for property offenses. The following table provides the joint distribution for military service and the commission of a property offense.
Property Offense No Property Offense Total
Military 208 753 961
No Military 1143 3389 4532
Total 1351 4142 5493
a) What are the independent and dependent variables in your study? How are they measured (nominal, ordinal, interval, ratio)?
Answer: IV:
DV:
b) Conduct a hypothesis test with a significance level of .01 to investigate the null hypothesis that the two variables are independent (not significantly related to one another). Be sure to identify the 5 steps of your hypothesis test and interpret your results accordingly.
Answer:
Step 1:
Step 2:
Step 3:
Cell Frequency Observed Frequency
Expected fo – fe (fo – fe) 2
A 208
B 753
C 1143
D 3389
Step 4:
Total =
Step 5:
c) Calculate the phi coefficient (F). What does this tell you?
Answer: F = =
3. Using the same example in question #2
a) Conduct a hypothesis test assuming that you have 10 times larger sample size (n=54,930)
* hint: you can answer this question without any additional calculation (You may simply indicate the things that change from the answers for question #2)
Answer:
Step 1:
Step 2:
Step 3:
Step 4:
Step 5:
b) Calculate the phi coefficient (F). What does this tell you?
Answer:
4. Using the same example in question #2
a) Conduct a hypothesis test with a significance level of .05
* hint: you can answer this question without any additional calculation (You may simply indicate the things that change from the answers for question #2)
Answer:
Step 1:
Step 2:
Step 3:
Step 4:
Step 5:
b) Calculate the phi coefficient (F). What does this tell you?
Answer:
Chapter 10: Hypothesis Tests involving Two Population Means or Proportions
1. Some criminologists argue there is a relationship between “impulsivity” and criminal offending. The idea is that impulsive people act on immediate gratification and that since crime involves quick pleasure and only the long-term possibility of any cost (getting caught and punished), it should be highly attractive to them. To test this notion you take a random sample of 120 people, you give them a personality test that includes a measure of impulsivity. Based on this test, you divide your sample into two groups: (1) the non-impulsive group (n = 80) and, (2) the impulsive group (n = 40). You then ask each person to report the number of criminal offenses they have committed in the last year. Finally, you calculate the mean number of self-reported offenses for each group, and here is the data you get:
Impulsive Non-Impulsive
n1 = 40 n2 = 80
= 13.5 = 10.3
s1 = 4.9 s2 = 4.0
a) What are the independent and dependent variables in your study? How are they measured (nominal, ordinal, interval, ratio)?
Answer: IV:
DV:
b) Test the null hypothesis that there is no difference between the two groups versus the alternative hypothesis that those who are impulsive commit more criminal offenses. Use an alpha of .01 and assume that the two population standard deviations are equal (s1 = s2), and make sure to properly interpret your results.
Answer:
Step 1:
H0:
HA:
Step 2:
Step 3: a =
df = (n1 – 1) + (n2 – 1) = n1 + n2 – 2 =
tcrit =
Reject the Null if
Step 4:
=
Step 5:
2. The following data show the number of unsafe needles used per week for a group of 7 heroin users before and after an AIDS education program. Your data is presented below.
Person Before
x1 After
x2 xD = x2 – x1
1 2 2 0 .428 .183
2 3 2 -1 -.572 .327
3 1 2 1 1.428 2.039
4 2 0 -2 -1.572 2.471
5 1 1 0 .428 .183
6 2 1 -1 -.572 .327
7 1 1 0 .428 .183
Total = –3 Total = 5.71
a) What are the independent and dependent variables in your study? How are they measured (nominal, ordinal, interval, ratio)?
Answer: IV:
DV:
b) Test the null hypothesis that the mean number of unsafe needles used after the education program is the same as the mean number before the program against the alternative that the mean number of unsafe needles after the program is less than the mean number before the program. Use an alpha of 0.05 and interpret your results.
Answer:
Step 1:
H0:
HA:
Step 2:
Step 3:
a =
df = (n – 1) =
tcrit =
Reject the null hypothesis if
Step 4:
Step 5:
