Problem Set# 2
1. Andy has started doing some research on his own (probably not a good thing), and he as found that some studies use a one-tailed t-test and others use a two-tailed t-test. In a short paragraph, help Andy understand the difference between a one-tailed t-test and a two-tailed t-test? Also, explain which test is preferred and why? (Pts. Possible 1)

2. Andy and Barney want to help their department save money. To do this, they start to look at the gas mileage of their vehicles. They want to start employing the vehicle that gets the best gas mileage to cut down on costs. The department currently has two types of cruisers, Dodge Chargers and Ford Explorers. Employing the Gas Mileage Data Set conduct a t-test to examine the difference in gas mileage between the Explorer (coded 0) and the Charger (coded 1). (Pts. Possible 3.5)
a. Should you conduct an Independent Sample T-test or a Paired Sample T-test and why? (.5 Pt.)
b. State a null and alternative hypothesis for your t-test based on the provided data. (1 Pt.)
c. For your selected t-test, are the four assumptions met, please describe how you know for each assumption? (1 Pt.)
d. Conduct your hypothesis test using both the p-value and confidence intervals approach. What do you find? Provide a brief summary of these findings to Andy with your suggestions. Finally, what does the confidence interval tell us about the population mean? Paste your SPSS output below your response. (1 Pt.)

3. Andy is currently evaluating the officers that he is hiring. His new officers typically come from one of three POST Satellite Academies (Utah Valley University, Weber State University, and Dixie State University). Andy has recently seen the officers’ performance scores from these academies, and wants to hire from the academy whose officers score the highest on their test. Using the Post Training dataset, examine the difference in means between officer performance for officers who graduated from UVU, WSU, and DSU. (Pts. Possible 4.5)
a. What statistical test should you conduct for this data? (.5 Pt.)
b. Can we assume homogeneity why or why not? If we cannot assume homogeneity which F-tests should we use (answer this question whether we have homogeneity or not)? (1 Pt.)
c. What does our F-test Statistic and ANOVA p-value tell us? Is there a statistically significant difference between the different academies? (1 Pt.)
d. Employing a Tukey test are any of our group means significantly different from each other? Use both the p-value and confidence intervals to examine the difference in means for each academy. Include your SPSS output below. (1 Pt.)
e. Include a printout of the Means Plot below. (.5 Pt.)
g. Provide Andy with a brief paragraph describing your findings and any recommendations you may have on the academies he should hire from. (.5 Pt.)

4. Andy has tasked you with analyzing how the monthly unemployment rate for the State of Utah influences the number of petty crime cases. Over the last 4 years, the unemployment rate in the state of Utah has continually decreased (excluding current pandemic). Andy suspects that this decrease in unemployment also influences the number of petty crimes in an area. Using the Petty Crimes set conduct your analysis. (5 Pts. Possible)
a. Using a scatterplot, graph your data putting the unemployment rate on the x-axis and crime cases on the y-axis. Paste your graph below and make sure to include the regression line on your graph. (.5 pt.)
b. What does your scatterplot tell you about the data, describe the direction of the relationship and the strength of the relationship based on what you see. Describe how the regression line is drawn? (.5 Pt.)
c. State a null and alternative hypothesis based on your graph and the data. (.5 Pt.)
d. Conduct a regression analysis and include your SPSS output below. (1 Pt.)
e. What are the b0 and b1 in the regression equation; display the equation below. (.5 Pt.)
f. Interpret the unstandardized coefficients in the regression coefficient. What does this mean to Andy; was he right? (1 Pt.)
g. Are the results statistically significant? How do you know? (.5 Pt)
h. What does the adjusted R-square tell us about our regression model? (.5 Pt)