STA 6167 – Spring 2012 – Exam 1 – PRINT Name __________________________
Note: Conduct all tests at = 0.05 significance level.
Q.1. A study was conducted to compare the effects of ad types (corporate social responsibility (CSR) and sex appeal (SA)) on people’s attitude toward the firm. There were 4 conditions, with 100 people being assigned to each condition (there were a total of 400 people in the study). The 4 conditions were:
1: CSR ad only 2: CSR ad + SA1 ad 3: CSR ad + SA2 ad 4: CSR ad + SA3 ad
p.1.a. Compute the Treatment and Error sums of squares and their degrees of freedom. (The overall mean is 58).
SST = _____________ df_{Treatments} = _____________ SSE = ______________ df_{Error} = ________________
p.1.b. Compute the test statistic and obtain the rejection region for testing H_{0}: _{}_{}_{}_{}
Test Statistic: ___________________________ Reject H_{0} if it falls in the range _______________________
Q.2. A multiple regression model was fit, relating consumer’s satisfaction of culinary (food) event (Y) to the following predictor variables/scales: food tasting (X_{1}), food/beverage prices (X_{2}), ease of coming/going to event (X_{3}), and convenient parking (X_{4}). The regression model was fit, based on n=277 respondents, with R^{2} = 0.44. The regression coefficients are given below, for the model: E(Y) = _{}X_{1}_{}X_{2}_{}X_{3} _{}X_{4}
p.2.a. Test H_{0}: Customer satisfaction is not associated with any of the predictors (_{}_{}_{}_{}).
p.2.a.i. Test Statistic:
p.2.a.ii. Reject H_{0} if the test statistic falls in the range __________________________________
p.2.b. Test H_{0}: Controlling for all other predictors, customer satisfaction is not associated with food/bev prices (_{}0).
p.2.b.i. Test Statistic:
p.2.b.ii. Reject H_{0} if the test statistic falls in the range __________________________________
Q.3. A oneway analysis of variance was conducted to compare 5 conditions in terms of respondents’ beliefs in paranormal activity. The responses are change scores in paranormal beliefs after being exposed to a television show about paranormal events (Positive values mean their beliefs increased, negative mean decreased. There were 22 people in each condition (for a total N=22(5) =110) and the Within Mean Square is MSE = 16. The conditions are (based on disclaimers prior to show):
1: Disclaimer that story in the show is based on reality, but is a reenactment (Mean_{1} = 1.0)
2: Disclaimer that the story in the show is purely fiction (Mean_{2} = 1.6)
3: Disclaimer that the story in the show is impossible (Mean_{3} = 2.0)
4: No Disclaimer (Mean_{4} = + 1.6)
5: No story shown (comedy show shown instead) (Mean_{5} = 0.8)
p.3.a. Compute Bonferroni’s minimum significant difference for comparing any 2 pairs of conditions:
p.3.b. Complete the following Table (and circle correct decision for each pair, where NSD = not significantly different):
Q.4. A linear regression model is fit, relating Y to 3 independent variables. The researcher is interested in determining whether any interactions are significant among the 3 independent variables. She fits the following 2 models (n = 30):
p.4.a. Compute the test statistic for testing H_{0}: No interactions among X_{1}, X_{2}, and X_{3} (_{}_{}_{})
p.4.b. Reject H_{0} if the test statistic falls in the range ____________________________________________
Q.5. For the following scenarios, fill in the missing values.
p.5.a. Multiple linear regression, n=32 subjects, p=6 predictor variables. Testing H_{0}: _{}_{}_{}_{}_{}_{}
Numerator df = ______________ Denominator df = ______________ Rejection Region: F_{obs} ____________
p.5.b. 1Way ANOVA (Completely Randomized Design), t treatments, r subjects/Trt.
Testing H_{0}: _{}_{}_{}Rejection Region: F_{obs} ≥ 3.490
# Treatments = t = _________________ # Replicates/Treatment = r = _______________
p.5.c. 2Way ANOVA (Randomized Block Design), t = 3 treatments, b = 6 blocks. Bonferroni’s Minimum Significant Difference (MSE = 300):
t_{.025,C,df} = ______________ =_________________________ B_{ij} = __________________
Q.6. A Randomized Block Design is conducted to compare t = 3 brands of puppy chow on weight gain of puppies. Three male puppies from 6 litters were selected, where the litters are blocks. Within litters, puppies are randomized so that one gets brand A, one gets brand B, and one gets brand C. Data are given in the following table (where the response is weight gain in a 3week period). Note that the total sum of squares is: TSS = 129.28
p.6.a. Given the following quantities, complete the ANOVA table (be careful of needed multipliers).
p.6.b. Conduct Friedman’s Test to determine whether there are differences among the brands on weight gain:
p.6.b.i. T_{1} = _________________________ T_{2} = _____________________ T_{3} = ________________________
p.6.b.ii. Test Statistic:
p.6.b.iii. Reject H_{0} if test statistic falls in the range _________________________________________
Q.7. All possible regressions are fit among models containing 3 potential independent variables. Complete the following table. The models are based on n=24 observations.
p.7.a. Complete the table. Note:
p.7.b. A researcher chooses the best model based on the SBC criterion. Which model will be selected? Why?
p.7.c. Another researcher chooses the best model based on C_{P, }which model is selected? Why?
