Published on October 21, 2008
Name (Please Print): STATISTICS 2010, Summer Quarter, 2008 Sample Final Exam (3 Problems) 1. The proportion of defective computers built by Byte Computer Corporation is 15% In an attempt to lower the defective rate, the owner ordered some changes made in the assembly process. After the changes were put into eﬀect, a random sample of 60 computers were tested revealing a total of 6 defective computers. Perform the appropriate test of hypothesis to determine whether the proportion of defective computer has been lowered. (Use α = 0.01) (a) The null hypothesis for this problem is H0 : p = 0.15, what is the appropriate alternative hypothesis? (b) Compute the critical value? (c) Calculate the value of the test statistic. (d) What is your conclusion? Do you reject the null hypothesis or fail to reject the null hypothesis? (e) Calculate a 99% conﬁdence interval for the population proportion. (f) Calculate a 90% conﬁdence interval for the population proportion.
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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