How do you test a hypothesis with categorical data?

Cnbyn1213
timer Asked: Feb 27th, 2018

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  1. 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.

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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:  2 obt   f o  f e 2       f e   Frequency Observed Cell A 14 B 6 C 8 D 22 Frequency Expected fo – fe (fo – fe) 2  f o  f e 2 fe Total = Step 5: c) Calculate the phi coefficient (Φ). What does this tell you? Answer: Φ = 2 n = 1 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: Step 4:  2 obt    f o  f e 2    f  e   Frequency Observed Cell A 208 B 753 C 1143 D 3389 Frequency Expected fo – fe (fo – fe) 2  f o  f e 2 fe Total = Step 5: c) Calculate the phi coefficient (Φ). What does this tell you? Answer: Φ = 2 n = 2 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 (Φ). 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 (Φ). What does this tell you? Answer: 3
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