Preparing for the final - sample questions with answers

Question 1 - Chi Square

You will test a hypothesis using two categorical variables and determine whether the independent variable has a statistically significant effect. You will be asked to state the null hypothesis. You will used supplied data to create an Observed frequencies table. You will use it to create an Expected frequencies table. You will be given a formula but should know the procedure. You will compute the Chi-Square statistic and degrees of freedom. You will be given formulas but should know the procedures by heart. You will use the Chi-Square table to determine whether the results support the working hypothesis. – Print and bring to class: Sample question: Hypothesis is that alarm systems prevent burglary. Random sample of 120 business with an alarm system and 90 without. Fifty businesses of each kind were burglarized. – Null hypothesis: No significant difference in crime between businesses with and without alarms Observed frequencies Expected frequencies

(50-57) 2 (70-63) 2 (50-43) 2 (40-47) = = 3.82 – Chi-Square = 3.82 – Df = (r-1) X (c-1) = 1 – Check the table. Do the results support the working hypothesis? No - Chi-Square must be at least 3.84 to reject the null hypothesis of no relationship between alarm systems and crime, with only five chances in 100 that it is true

Question 2 - Difference Between the Means (t-Test)

You will be given scores and variances for two samples and asked to decide whether their means are significantly different. You will be asked to state the null hypothesis. You will then compute the t statistic. You be given formulas, but should know the methods by heart. Please refer to week 15 slide show. You will be given the variances. To compute the t you will compute the pooled sample variance and the standard error of the difference between means. You will then compute the degrees of freedom (adjusted sample size) and use the t table to determine whether the coefficient is sufficiently large to reject the null hypothesis. – Print and bring to class: – Use the one-tailed test if the direction of the effect is specified, or two-tailed if not You will be asked to express using words what the t-table conveys about the significance (or non-significance) of the t coefficient Sample question: Are male CJ majors significantly more cynical than female CJ majors? We randomly sampled five males and five females. Males: 4, 5, 5, 3, 4 Females: 4, 3, 4, 4, 5 – Null hypothesis: No significant difference between cynicism of males and females – Variance for males (provided): 0.7 Variance for females (provided): 0.5 – Pooled sample variance =.6 SE of the difference between means =.49 t =.41 df = 8 – Check the “t” table. Can you reject the null hypothesis? NO – Describe conclusion using words: The t must be at least 1.86 (one-tailed test) to reject the null hypothesis of no significant difference in cynicism, with only five chances in 100 that it is true.

Question 3 - Interpreting a table

The final exam will ask the student to interpret a table. The hypothesis will be provided. Student will have to identify the dependent and independent variables Students must recognize whether relationships are positive or negative Students must recognize whether relationships are statistically significant, and if so, to what extent Students must be able to explain the effects described by log-odds ratios (exp b) using percentage Students must be able to recognize and interpret how the effects change: – As one moves across models (different combinations of the independent variable) – As one moves across different levels of the dependent variable For more information about reading tables please refer to the week 14 slide show and its many examples IMPORTANT: Tables must be interpreted strictly on the techniques learned in this course. Leave personal opinions behind. For example, if a relationship supports the notion that wealth causes crime, then wealth causes crime! Sample question and answer on next slide

Hypothesis: Unstructured socializing and other factors  youth violence 1.In which model does Age have the greatest effect? Model 1 2.What is its numerical significance? Use words to explain #2 Less than one chance in 1,000 that the relationship between age and violence is due to chance 4.Use Odds Ratio (same as Exp b) to describe the percentage effect of Age on Violence in Model 1 For each year of age increase, violence is seventeen percent more likely 5.What happens to Age as it moves from Model 2 to Model 3? What seems most responsible? Age becomes non-significant. Most likely cause is introduction of variable Deviant Peers.