STA 6166 – Fall 2008 – Exam 2 PRINT NAME _____________________Ford wants to compare mean assembly times for Explorer’s at their 3 assembly plants. They observe random samples of 10 cars at each plant, and obtain the following summary statistics on assembly times (in minutes):Plant Mean Std. Dev.Atlanta 180 12Chicago 185 10Detroit 175 9(a) Compute the between plant (Treatment) sum of squares and its degrees of freedom(b) Compute the within plant (Error) sum of squares and its degrees of freedom(c) Compute the test statistic(d) Conclude that the population means differ ( if the test statistic is __________A researcher wishes to compare two species of ferns with respect to chemical uptake. She samples 10 ferns of each species, and measures the amount of the chemical uptake in each of the 20 specimens. The summary statistics and relevant quantities are given below (she finds no evidence to believe the population variances are equal):a) Give a 95% confidence interval for the difference in true (population) means for the 2 species.b) The rank sums for the 2 species are T1=140 and T2=70, respectively. Use the normal approximation for the Wilcoxon Rank-Sum test to test whether the population means differ at the 0.05 significance level. Give the test statistic and give the P-value for your statistic.A study was conducted to measure the effect of a new training program for new employees at a large company. A sample of 9 new employees were selected and given a test regarding ethics in the workplace before and after a1-day training session on ethics was given. For each employee, the difference between the scores (After – Before) was obtained. The mean and standard deviation of these differences were 15.0 and 9.0, respectively. Testto determine whether the training course is effective in increasing true mean scores:a) Null Hypothesis: D 0 Alternative Hypothesis: D 0b) Test Statistic: c) Rejection Region: Do we conclude that the training course is effective in increasing true mean scores at the =0.05 significance level? Yes or NoA One-Way Analysis of Variance is conducted to compare the effects of 3 insecticides. The sample mean kill rates for 8 replicates of each insecticide are 24, 36, and 40, respectively. The MSE from the ANOVA is 100. Compute Bonferroni’s B, and determine which insecticides (if any) differ significantly (at the experiment-wise error rate of =0.05). Note the appropriate critical value is t.025,3,21=2.601An textile engineer is interested whether the variation in breaking strength of Yarn Type A is larger than the variation in Type B. Random samples of nA=nB=7 measurements were obtained, and the sample variances were sA2=5.0 and sB2=1.25. Do the data provide sufficientevidence to conclude A2 > B2 ? Test by using = 0.05.a) Test Statistic:b) Rejection Region:c) The P-value is Larger or Smaller than 0.05.A researcher wishes to estimate the difference within E=4.0 with 95% confidence. Past experience has found that the standard deviation of each of the populations is 20. How many measurements will they need to take from each
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