Applied Statistics Read each of the research scenarios and answer the questions. 1. A group of student researchers believe that there is a relationship between attitudes toward social issues (110) and amount of political activity (0-15). The group surveyed students (N=102) at the union every day for an entire semester about their attitudes toward social issues (M=6.14, SD=1.07) and recorded the number of political events attended on campus (M=8.69, SD=2.51). (Total 28 pts) A. What are the independent and dependent variables and how are each scaled (1 pt each; Total 4 pts)? Independent:________________________ Scaling:_____________________________ Dependent:__________________________ Scaling:_____________________________ B. What test should the students use (4 pts)?__________________________________________________ C. Why that test (2 pts)? D. What are the null and alternative hypotheses for that test (4 pts)? E. What are that tests assumptions (2 pts)? F. What are the df (2 pts)?________________________ G. What is the critical value for p=.05 (2 pts)? _________________________ H. If the students calculate a test statistic of .31, should they (2 pts)? I. Interpret the findings (6 pts): Retain H0 Reject H0 2. Researchers know that the average rate of violence within intimate relationships is 20 men or women per minute in the US (SD=2.47), according to the National Coalition against Domestic Violence (NCADV). The local chapter of the NCADV is concerned about area rates of domestic violence because the local average is 23.20 (N=265). They would like to determine if the local rate is the same as the national rate. (Total 29 pts) A. What are the independent and dependent variables and how are each scaled (1 pt each; Total 4 pts)? Independent:________________________ Scaling:_____________________________ Dependent:__________________________ Scaling:_____________________________ B. What test should be used (4 pts)?__________________________________________________ C. Why that test (2 pts)? D. What are the null and alternative hypotheses for that test (4 pts)? E. What are that tests assumptions (3 pts)? F. What are the df (2 pts)?________________________ G. What is the critical value for p=.05 (2 pts)? _________________________ H. If the researchers calculate a test statistic of 1.78, should they (2 pts)? I. Interpret the findings (6 pts): Retain H0 Reject H0 3. Dr. Anders believes that the size of coffee selected at Starbucks (1=Tall, 2=Grande, and 3=Venti) and whether the drink is caffeinated (1=No Caffeine, 2=Regular Caffeine, and 2=Extra Caffeine) impacts people's mood in her classes (scores range from 1 negative mood-7 positive mood). She collects data from the 360 students in her classes. (Total 50 pts) A. What are the independent and dependent variables and how are each scaled (1 pt each; Total 6 pts)? Independent:________________________ Scaling:_____________________________ Independent:________________________ Scaling:_____________________________ Dependent:__________________________ Scaling:_____________________________ B. What test should Dr. Anders use (4 pts)?__________________________________________________ C. Why that test (2 pts)? D. What are the null and alternative hypotheses for that test (12 pts)? E. What are that tests assumptions (3 pts)? Dr. Anders calculates the appropriate test and rejects H0 for the effect of coffee size (test value of 3.69, df= 2 and 352) and the effect of caffeine (test value of 5.72, df= 2 and 352) but retains H0 for the combination of the two (test value of 1.75, df= 5 and 352). Below are the means (standard deviation) *indicates a difference: No Caffeine Regular Extra Caffeine Caffeine Tall 3.14 (.87) 4.52 (.99) 5.94 (1.01) Grande 2.87 (.74) 4.29 (.51) 5.21 (.94) Venti 3.58 (1.11) 4.71 (1.20) 5.62 (.95) 3.20 (.91)* 4.51 (.90) 5.59 (.97)* F. Draw at least one graph to represent the data (5 pts) Total 4.53 (.96) 4.12 (.73)* 4.64 (1.09)* G. Interpret the findings (18 pts): 4. Bibliotherapy is a common tool to use with children who have a hard time bonding with a therapist and opening up during therapy sessions. Dr. Contos wants to examine if children who participate in bibliotherapy (M=16.48, SD=2.67) score lower on levels of anxiety (0-25) than children who participate in play therapy (M=18.11, SD=2.58). She interviews 25 children in each group for a total of 50 children. (Total 29 pts) A. What are the independent and dependent variables and how are each scaled (1 pt each; Total 4 pts)? Independent:________________________ Scaling:_____________________________ Dependent:__________________________ Scaling:_____________________________ B. What test should Dr. Contos use (4 pts)?__________________________________________________ C. Why that test (2 pts)? D. What are the null and alternative hypotheses for that test (4 pts)? E. What are that tests assumptions (3 pts)? F. What are the df (2 pts)?________________________ G. What is the critical value for p=.05 (2 pts)? _________________________ H. If Audi calculates a test statistic of 4.76, should they (2 pts)? Retain H0 Reject H0 I. Interpret the findings (6 pts): 5. The average amount spent on a new car in 2015 was $33,560 with a standard deviation of $11,194. You just bought a new car for $18,422 and want to know if you got a good deal compared to the national average. (Total 25 pts) A. What are the independent and dependent variables and how are each scaled (1 pt each; Total 4 pts)? Independent:________________________ Scaling:_____________________________ Dependent:__________________________ Scaling:_____________________________ B. What test should you use (4 pts)?__________________________________________________ C. Why that test (2 pts)? D. What are the null and alternative hypotheses for that test (4 pts)? E. What are that tests assumptions (2 pts)? F. What is the critical value for p=.05 (2 pts)? _________________________ G. If you calculate a test statistic of 1.97, should she (2 pts)? H. Interpret the findings (5 pts): Retain H0 Reject H0 6. Dr. Barrett has run a test to predict verbal abilities (0-8) from number of siblings (0-6). He thinks that the more people you have to talk to when you are young (number of siblings) the more verbal you will be. He has already run the test in SPSS and below is the output. (Total 21 pts) VerbalAbility Siblings Model 1 Regression Residual Total Mean 4.25 3.45 SD 1.963 1.817 Sum of Squares 181.874 45.376 227.250 Model 1 (Constant) Siblings N 60 60 df Mean Square F 1 181.874 232.470 58 .782 59 Unstandardized Standardized Coefficients Coefficients B Std. Error Beta .917 .247 .966 .063 .895 Sig. .000a t 3.717 15.247 Sig. .000 .000 A. What are the independent and dependent variables and how are each scaled (1 pt each; Total 4 pts)? Independent:________________________ Scaling:_____________________________ Dependent:__________________________ Scaling:_____________________________ B. What test should Dr. Barrett use (4 pts)?__________________________________________________ C. Why that test (2 pts)? D. For the Independent Variable (2 pts): Mean___________ Standard Deviation_________________ E. For the Dependent Variable (2 pts): Mean___________ Standard Deviation_________________ F. Should Dr. Barrett (2 pts)? H. Interpret the findings (5 pts): Retain H0 Reject H0 7. Dr. Henry believes that if he gives couples a measure of relationship satisfaction (0-8) before he provide them couples therapy and then the same measure of relationship satisfaction (0-8) after therapy his patients will be less likely to divorce. He give his 41 clients the satisfaction measure then therapy for one month and gives the same 41 clients the satisfaction measure after therapy. (Total 18 pts) A. What are the independent and dependent variables and how are each scaled (1 pt each; Total 4 pts)? Independent:________________________ Scaling:_____________________________ Dependent:__________________________ Scaling:_____________________________ B. What test should Dr. Henry use (2 pts)?__________________________________________________ C. Why that test (1 pts)? D. What are the null and alternative hypotheses for that test (2 pts)? E. What is the critical value for p=.05 (1 pts)? _________________________ G. If Dr. Henry calculates a test statistic of 2.11, should he (2 pts)? H. Interpret the findings (6 pts): Retain H0 Reject H0