STA 6166 – Exam 1 – Spring 2016 PRINT Name _________________________Unless stated otherwise, conduct all tests at = 0.05 significance level.True/False, Multiple Choice, and Fill in the Blanks QuestionsQ.1. Two researchers analyze the same set of observations from 2 samples of equal sample sizes (n1 = n2 = n).One researcher uses the independent sample t-test, based on equal variances. The other researcher uses the independentsample t-test, based on unequal variances. Choose the correct answer:- Their test statistics will be the same, their degrees of freedom will be the same. - Their test statistics will be the same, their degrees of freedom will be different.- Their test statistics will be different, their degrees of freedom will be the same.- Their test statistics will be different, their degrees of freedom will be different.Q.2. A scientist wants to compare the effects of 3 treatments on behavior in mice. The treatments are: 1) Placebo, 2) Drug A, 3) Drug B. The experiment is balanced. The researcher is interested in 2 specific contrasts:Contrast 1: Placebo (1) versus Average of Drug A (2) and Drug B (3), Contrast 2: Drug A versus B. Give the twocontrasts (note there are many ways of writing these, but they share a specific pattern):1 1 2 3 2 1 2 3______ ______ ______ ______ ______ ______l lm m m m m m= =Q.3. A study is conducted to compare 2 methods of teaching foreign language to children (independent samples). Oneanalyst uses a 2-sided test of H0: = 0 versus HA: ≠ 0 based on the independent sample t-test, assumingequal variances. The other analyst uses a 1-Way Analysis of Variance F-test to test H0: versus HA: ≠.They use the same computing software, so there are no issues due to rounding. Choose the correct answer: The p-value from the t-test will always be higher than the p-value from the F-test The p-value from the t-test will always be lower than the p-value from the F-test The p-value from the t-test will always be the same as the p-value from the F-test None of the aboveQ.4. For a balanced 1-Way ANOVA, with t > 2 groups, when making all pairwise comparisons, Tukey’s W will always besmaller than Bonferroni’s B.TRUE or FALSEProblemsQ.5. Among 2 large populations (Males and Females) who completed the Rock and Roll marathon in 2015, thepopulation means and standard deviations of velocities (miles per hour) were: 6.34 1.06 5.84 0.83M M F Fm s m s= = = =Suppose you simultaneously took many random samples of size nM = nF = 20 from each population, and for each pair ofrandom samples, you computed M FY Y- and saved each difference.p.5.a. What would you expect the mean of the M FY Y- values to be.p.5.b. What would you expect the standard deviation of the M FY Y- values to be.p.5.c. Between what 2 bounds would you expect 95% of the M FY Y-values to lie between?Q.6. Two models of video cameras are being compared for detecting animals in a wildlife setting. The cameras will filmthe same locations in fixed time intervals in a paired difference experiment. The parameter D is the population meandifference across all possible locations in the fixed time intervals. From a pilot study, it is believed d = 5. How manysamples will be needed if we wish for the margin of error in estimating D within E = 0.5 with 95% Confidence?Q.6. An experiment is conducted to compare breaking strengths of 2 types of fibers. The means, standard deviations, andsample sizes of random samples from each fiber type are: 1 1 2 21 250 12 10 45 8 10y s n y s n� �= = = = = =p.6.a. Test H0: 12 = 22 versus HA: 12 ≠ 22 at = 0.10 significance levelTest Statistic: ________________ Reject H0 if Test Statistic < ___________ or > ___________p.6.b. Regardless of your previous answer, assume12 = 22, Test H0: 1 - 2 = 0 versus HA: 1 - 2 ≠ 0 ( ) ( )2 210 1 12 10 1 813.2710 10 2- + -=+ -Test Statistic: ________________ Reject H0 if Test Statistic < ___________ or > ___________Q.7. A 1-Way ANOVA is conducted, comparing clarity of t = 3 methods if meniscal repair. A sample of N=18 subjects wasobtained and assigned at random such that n1 = 6 received method 1, n2 = 6 received method 2, and n3 = 6 receivedmethod 3. The response was Y = Displacement (mm). Complete the following table to test:0 1 2 3: vs : Not all are equalA iH Hm m m m= =Do we reject the null hypothesis? Yes or No Is the P-value < 0.05 or > 0.05Q.8. A study is conducted to compare lifetimes of 2 brands of light bulbs. Random samples of n1 = n2 = 20 are obtainedfrom each manufacturer. Due to the highly skewed distributions of lifetimes, the large-sample Wilcoxon rank-sum test wasused. The investigators tested each bulb, measuring its lifetime, and ranked all of the N = 40 bulbs. The rank sum for thetwo brands are T1 = 460 and T2 = 360. Complete the following parts to test H0: M1 = M2 HA: M1 ≠ M2p.8.a. Compute T:p.8.b. Compute T:p.8.c. Test Statistic: p.8.d. Rejection Region: _____________________________ p.8.e. Reject H0? Yes or NoQ.9. An experiment was conducted to compare wine color intensity (Y) among t = 6 types of wine barrels. There 9replicates for each of the wine barrel types. The Mean Square Error (MSW) was 1.04.p.9.a. Compute Tukey’s Honest Significant Difference for Comparing all pairs of wine barrel typesConclude Conclude if ______________________i j iji jy y Wm m� - � = p.9.a. Compute Bonferroni’s Minimum Significant Difference for Comparing all pairs of wine barrel typesConclude Conclude if ______________________i j iji jy y Bm m� - �
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