Statistical Analysis: Practice Problems for Exam 3 - Prof. Lawrence Herman Winner, Exams of Data Analysis & Statistical Methods

Download Statistical Analysis: Practice Problems for Exam 3 - Prof. Lawrence Herman Winner and more Exams Data Analysis & Statistical Methods in PDF only on Docsity! STA 6166 – Practice Problems – Exam 3 A study is conducted to compare whether incidence of muscle aches differs among athletes exposed to 5 types of pain medication. A total of 500 people who are members of a large fitness center are randomly assigned to one of the medications. After a lengthy workout, each is given a survey to determine presence/absence of muscle pain. For the 5 groups: 25, 38, 32, 40, and 35 are classified as having muscle pain, respectively. The following output gives the results for the Pearson chi-square statistic for testing (=0.05): H0: True incidence rate of muscle pain doesn’t differ among medications HA: Incidence rates are not all equal Test Statistic _________________________ Reject H0 if the test statistic falls in the range(s) ________________________ P-value _____________________________ Conclude (Circle One): Medication effects not all equal No differences in effects Give the expected number of incidences of muscle pain for each medication under H0: In a 2-Factor ANOVA, measuring the effects of 2 factors (A and B) on a response (y), there are 3 levels each for factors A and B, and 4 replications per treatment combination. Give the values of of the F-statistic for the AB interaction for which we will conclude the effects of Factor A levels depend on Factor B levels and vice versa (=0.05): Chi-Square Tests 6.150a 4 .188Pearson Chi-Square Value df Asymp. Sig. (2-sided) A simple linear regression model is fit, relating plant growth over 1 year (y) to amount of fertilizer provided (x). Twenty five plants are selected, 5 each assigned to each of the fertilizer levels (12, 15, 18, 21, 24). The results of the model fit are given below: Can we conclude that there is an association between fertilizer and plant growth at the 0.05 significance level? Why (be very specific). Give the estimated mean growth among plants receiving 20 units of fertilizer. The estimated standard error of the estimated mean at 20 units is 46.0 450 )1820( 25 1 1.2 2    Give a 95% CI for the mean at 20 units of fertilizer. Coefficientsa 8.624 1.810 4.764 .000 .527 .098 5.386 .000 (Constant) x Model 1 B Std. Error Unstandardized Coefficients t Sig. Dependent Variable: ya. 1. A study compared St. John’s Wort (SJW), Sertraline, and placebo in patients with major depressive disorder. Patients were assigned at random to one of the three treatments and were classified as having any response or no response. The contingency table is given below. Trt \ Outcome Any Response No Response Total SJW 43 70 113 Sertraline 53 56 109 Placebo 50 66 116 Total 146 192 338 a) Give the conditional distributions for each treatment and overall. Trt \ Outcome Any Response No Response Total SJW 100% Sertraline 100% Placebo 100% Total 100% b) Give the expected count for Any Response among SJW patients under the hypothesis of no association between response and treatment. 2. A study considered the occurrence of upholstery in households in Philadelphia during 4 time periods. The following table gives a cross-tabulation of period by upholstery for samples of households within the periods. PERIOD * UPHOLSTE Crosstabulation Count UPHOLSTE TotalNo Yes PERIO D 1 61 19 80 2 68 14 82 3 64 18 82 4 53 27 80 Total 246 78 324 a) Give the expected number of Yes in Period 1 under the hypothesis that upholstery occurrence is independent of period. b) Give the contribution for that cell to the chi-square statistic. 2. A consumer is interested in comparing prices among 3 grocery store chains in his city. He randomly samples 8 branded products and obtains the regular price of each product at each store. He finds that between store variation accounts for 20% of the total variation and between product variation accounts for 60% of the total variation. (a) Complete the following ANOVA table. Source DF SS MS Fobs Stores Products Error Total 24-1=23 600 (b) Test whether we can conclude that the population mean prices differ among the three stores by completing the following sentence (use =0.05 significance level and circle any correct bold type options and fill appropriate numeric values in the blanks). Conclude / Do Not conclude means differ since ____ is above / below ________ (c) This is an example of dependent samples because (circle the best answer): i. The sample sizes for each store are the same ii. The same products are observed at each store iii. There are 3 stores 3. A Randomized Block Design is used to compare 3 types of sounds on sleep in 9 people suffering from sleeping disorders. Each subject is assigned to each sound type (in random order) and the time until the person falls asleep is measured The following calculations are obtained from a statistical software program. 5.112506040 321  MSExxx Use Bonferroni’s method to obtain simultaneous 95% confidence intervals for all pairs of population means. Give the correct conclusion based on the intervals (NSD=”Not significantly different). Sounds Point Estimate Confidence Interval Conclude 1 vs 2  1 vs 3 2 vs 3 1. Interaction terms are needed in a Two-way ANOVA model when (circle any correct answer(s)): a) Each explanatory variable is associated with the response. b) The difference in means between two categories of one explanatory variable varies greqatly among the levels of the other explanatory variable. c) The mean square for the interaction term is much larger than the mean square error. 2. A researcher is interested in comparing children from 3 different cultures with respect to their math skills. She samples children from each of the cultures, obtains their age and gives each of them a standardized math exam. This would best be described as a: a) 2-Factor ANOVA b) 1-Way ANOVA with dependent samples (Randomized Block Design) c) Repeated Measures ANOVA with two Factors d) Analysis of Covariance 3. In the model E(Y) =  +  X + 1Z1 where Z1 is a dummy variable identifying individuals in group 1 (circle any correct answer(s)): a) The qualitative predictor has two levels b) One line has slope  and the other line has slope 1 c) 1 is the difference in the sample means for groups 1 and 2 d) 1 is the difference in the adjusted means (controlling for X) for groups 1 and 2 4. A researcher is interested in comparing 4 computer search engines in terms of search times for his research assistants. He gives his assistants lists of items to be researched and measures the amount of time taken to complete the list. Because he knows there is a large amount of variability in his assistants’ typing and analytical skills, he has each assistant use each search engine. This would best be described as a: e) 2-Factor ANOVA f) 1-Way ANOVA with dependent samples (Randomized Block Design) g) Repeated Measures ANOVA with two Factors h) Analysis of Covariance 5. The following partial ANOVA table was obtained from a 2-way ANOVA where three advertisements were being compared among men and women. A total of 30 males and 30