Information about Stat2010 Sample Final

Published on October 21, 2008

Author: knksmart

Source: slideshare.net

2. A customer was interested in comparing the top speed (in miles per hour) of two models of snowmobiles. For testing the following pair of hypotheses H0 : µ1 − µ2 = 0 vs. H1 : µ1 − µ2 = 0 the customer selected two independent random samples of the snowmobiles and calculated the following summary information: (Use α = 0.05) Model 1 Model 2 Sample Size (n) 8 9 Sample Mean (¯) x 90 84 Sample Standard Deviation (s) 3 5 (a) Compute the critical value(s) for this test. (b) Calculate the pooled variance. (c) Calculate the value of the test statistic. (d) What is your conclusion? (e) Calculate a 95% conﬁdence interval for the diﬀerence in means, µ1 − µ2 .

3. In order to determine whether good looks translate into heftier paychecks, an economist collected data on the annual income of 25 doctors (y) in hundreds of thousands of dollars and attractiveness (x) as recorded on a scale from 1 to 5, based on a panel’s rating of head-and-shoulder photographs. x = 3.2 y = 3.6 s2 = 1.8 x s2 = 4.4 y sxy = 2.6 (a) Determine the least squares regression line. (b) Calculate the sum of squares for error, (SSE), and the standard error of estimate, s . (c) Calculate the estimated standard error of the slope coeﬃcient, sb1 . (d) Calculate a 95% conﬁdence interval estimate for β1 .

(e) Test the following hypotheses at the α = 0.05 level of signiﬁcance. H0 : β1 = 0 vs. H1 : β1 = 0 i. What are the critical values that set up the rejection regions? ii. What is the value of the test statistic? iii. What is your conclusion? Does a linear relationship exist between the two variables? (f) Find the predicted annual income given an attractiveness score of 4.

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