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Questions:

Question 15 [ Which of the following statements about simple linear regression are true? There may be more than one correct statement; check all that area true. l_l a} If r = 0.5, then the sample slope will be positive. l_,l b} If all points in a sample fall perfectly on a line with a positive slope, then r = 1. l_,l c) Least squares regression chooses the regression line that minimizes 20'} X02- l:_l cl) If we wish to investigate whether there evidence of a linear relationship between Xand Y, the null hypothesis of the most appropriate test is H0 2 ,60 = 0. Question 16 Suppose we are about to draw a sample from a normally distributed population, and find a confidence interval for the population mean. Which one of the following statements is true? C1 The tapproach is always used when the population standard deviation is known. A 99% confidence interval will be wider than the corresponding 95% interval calculated on the same data. (:1 All else being equal, the greater the variance, the smaller the margin of error. ("'j, 95% of the observations in the sample will fall within the 95% confidence \\./ interval we calculate. ("'j, If we use a zvalue when calculating the interval when we should be using 1', the \\./ '_ resulting interval will be too wide. Question 17 Researchers investigated the failure time of bearings treated with 5 different compounds. As part of the procedure, they carried out an ANOVA, testing the null hypothesis that all 5 compounds have the same true mean failure time. In the ANOVA, they found a p-value of 0.00018, and decided to apply the Tukey procedure to find confidence intervals for the pairwise differences in means at a family-wise confidence level of 95%. The results of the Tukey procedure are given below. ("lwr" is the lower bound of the interval, "upr" is the upper bound.) How many of these pairwise differences are statistically significant? (No calculations required!) 1wr upr B-A -0. 782 1. 043 C-A -0. 929 0. 896 0. 010 1.835 E-A 0. 302 2. 127 C-B -1. 059 0.766 D-B -0. 121 1. 704 E-B 0. 172 1.997 D-C 0. 026 1. 851 E-C 0. 319 2. 144 E-D -0. 620 1.205 O2 3 4 0 5 06