MidtermI_2008_PracticeExamI - Practice Midterm Exam for...

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1 Practice Midterm Exam for Stat 102 Instructions : The exam itself will be a semi-closed book exam. One page of notes (or one page - two-sided) will be allowed. When performing hypothesis tests, clearly state the null and alternative hypotheses and show the critical value and/or P-value (from the table) where appropriate. Normal tables, t-tables and F-tables copied from your text are provided. Write your answers on the test and always show your work. Partial credit will be given. Time: 90 minutes . 1. When gasoline is pumped into the tank of an automobile, hydrocarbon vapors in the tank are forced out and into the atmosphere. This is undesirable, and vapor-recovery devices are usually installed on gasoline pumps in order to reduce the emission of these vapors. It is difficult and expensive to test a recovery device in actual operation, and so tests of new devices typically involve only a modest number of trials of the device. Data was gathered measuring the hydrocarbon emissions while filling a gas tank for two types of vapor-recovery device: a “regular” device and a new, “improved” design. The following analysis is for a sample of 50 observations of hydrocarbon emissions (in g) using the new and hopefully improved type of device, and 75 observations using the standard device. Here is a table from JMP showing the means and standard deviations of the two samples: Means and Std Deviations Level Number Mean Std Dev Std Err Mean Lower 95% Upper 95% Improved 50 28.46 6.178 0.8737 26.70 30.22 Regular 75 31.99 9.232 1.0660 29.86 34.11 Does the “improved” design appear to change the level of hydrocarbon vapors emitted? Set up appropriate hypotheses and carry out the test at 0.05 level. [You may use whichever method seems appropriate to you – the equal population variance method or the unequal population variance method. If you use the latter method, you may assume its DF number is DF 100.]
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2 2. In the same experiment as in problem 1, the temperature of the dispensed gas ( ° F) was measured for each trial. Here is the scatterplot and the analysis for the 75 observations using the regular type of device: Bivariate Fit of Emitted Hydrocarbons By Dispensed temp 15 20 25 30 35 40 45 50 55 60 Emitted Hydrocarbons 30 40 50 60 70 80 90 Dispensed temp Linear Fit: Emitted Hydrocarbons = -0.137 + 0.546 Dispensed temp Summary of Fit RSquare _______ Root Mean Square Error 4.40 Mean of Response 31.99 Observations 75 Analysis of Variance Source DF Sum of Squares Mean Square F Ratio Model _____ _______ 4896.5 _______ Error _____ _______ _____ Prob > F C. Total _____ 6307.0 <.0001 Parameter Estimates Term Estimate Std Error t Ratio Prob>|t| Intercept -0.137 2.08 -0.07 0.948 Dispensed temp 0.546 0.0343 15.92 <.0001
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This note was uploaded on 04/04/2012 for the course STAT 102 taught by Professor Shaman during the Spring '08 term at UPenn.

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MidtermI_2008_PracticeExamI - Practice Midterm Exam for...

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