Virginia Commonwealth University Probability Statistics Questions

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Virginia Commonwealth University

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9- 2 points Completely interpret the SPSS output below from a study of the time it takes rats to run through a maze to get a piece of cheese behind a Black, Red, or Green door at the end. [Hint: begin your answer with “We are ___% confident that…”, with the appropriate value in the blank and the remaining details added afterwards.] 10 – points Dean wishes to determine if the mean cost of new Chevrolet vehicles is the same for the five Chevrolet dealerships in his city. The same seven vehicles (year, make, and model) were priced at the five dealerships. Why is it important to treat the vehicles as blocks in this scenario? 11-6 points Consider the following partial RBD ANOVA table. Complete the accompanying partial One-Way ANOVA table for the same study if it were decided that blocks should not be used. RBD ANALYSIS OF VARIANCE Sum of Source DF Squares Dealership 4 2.9483 Vehicle (Blocks) 6 247.3979 Error 24 1.7322 Total 34 252.0784 Source ONE-WAY ANALYSIS OF VARIANCE Sum of DF Squares Dealership _____ __________ Error _____ __________ Total _____ __________ [DF for Dealership =Question Blank][DF for Error =Question Blank][DF for Total =Question Blank][SS for Dealership =Question Blank][SS for Error =Question Blank][SS for Total =Question Blank] 13- (10 points) A psychologist believes that the frequency that a person engages in sexual activity depends upon what type of relationship that person may be in. She sampled 1772 randomly selected adults and asked them what type of relationship they were in and how often per week they engaged in sexual activity. Do the data support her hypothesis? Use the SPSS output below to perform the appropriate six-step test at the 5% significance level using the P-value approach. 14- 15 points The U.S. Bureau of Prisons publishes data in Statistical Report on the times served by prisoners released from federal institutions for the first time. Independent random samples of released prisoners for five different offense categories yielded the following information on time served, in months. Offense Counterfeiting Drug Laws Firearms Forgery Fraud ni 13 13 13 13 13 x̄ i 14.5 18.4 18.2 15.6 11.5 si 4.5 3.8 4.5 3.6 4.7 Part a: (9 points) Do the data provide sufficient evidence at the 1% significance level to conclude that a difference exists in mean time served by prisoners among the five offense groups? Show all steps of the appropriate test procedure. Be sure to list any assumptions that are assumed to be true (do not create any plots). Part b: (4 points) Use Tukey-Kramer (Tukey’s W) to determine any differences in the mean time served by prisoners among the five offense groups (be sure to include an underline graphic and sentence), or explain why you don’t think there is a difference in the mean time served by prisoners among the five offense groups. Part c: (2 points) Which offense group(s) do you think yield the shortest mean time served? Be sure to include information from your analysis above as the basis for your answer. Upload a single PDF of your complete solution (all 3 parts) to this By-Hand exercise in the box below. 15- 10 points (By-Hand) The following SPSS output is for an experiment to measure how the quality of steel, measured by ELAST, an index of quality, is affected by two aspects of a processing procedure: CLEAN: concentration of a cleaning agent, and TEMPR: an index of temperature and pressure. Perform only appropriate ANOVA and multiple comparison analyses for this Two-way ANOVA experiment. Please use a 5% significance level (α = 0.05). 6Suppose you have a One-way ANOVA experiment with 7 treatments and 16 observations per treatment, and you fail to reject the null hypothesis. How many pairwise comparisons will you make? 7 16 21 112 None are needed. 7- In a Two-way ANOVA experiment with 4 levels of Factor A, 3 levels of Factor B, and m = 3 observations per treatment combination, the degrees of freedom for the A*B interaction term is... 3 4 6 112 not defined ONE-WAY ANALYSIS OF VARIANCE Source DF Sum of Squares Dealership 4 2.9483 Error 30 249.1301 Total 34 252.0784
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