practice_final_s09

# practice_final_s09 - Engineering Statistics ENGRD2700...

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Engineering Statistics ENGRD2700 PRACTICE PROBLEMS FOR FINAL EXAM Spring 2009 Note : Our ﬁnal is 2.5 hours and closed note. These are relevant practice problems compiled from last term. Our format will be more like our ﬁrst two exams and will be shorter than what is here. Solutions will be posted next week. 1. Like many states, Pennsylvania holds a daily lottery. People buy lottery tickets and try to guess which three-digit number (000 through 999) will be picked each evening at 7 p.m. during a televised drawing. The winning lottery number is produced from three separate machines (one for each digit) that contain 10 Ping-Pong balls, labelled 0 through 9. The balls are blown about in a container by a jet of air and mixed. Then one is sucked through an opening at the top of the machine. The digit on that ball becomes the selected digit. In 1980, when there was concern that the PA lottery was “ﬁxed”, the contention was that all the Ping-Pong balls except the 4’s and 6’s had been weighted down (injected with white paint using a hypodermic needle) so as to be less likely to be chosen. (a) If the lottery is fair, what is the probability that the 3 digit number contains no digits other than 4 or 6 ? (b) In 1200 consecutive drawings, on 15 occasions the 3 digit number contained no digits other than 4 or 6. Would you say this was good evidence that the lottery was “ﬁxed”? Give your reasoning. [Hint. Set this up as a hypothesis testing problem, clearly stating the hypotheses.] Note . On 24 April 1980, the number 666 came up, resulting in \$1.18 million going to 8 people in on the scam. The TV broadcast host Nick Perry and Lottery district manager Edward Plevel both received prison terms. Twenty years later, Hollywood released a movie loosely based on the scandal, ”Lucky Numbers,” starring John Travolta (and Michael Moore). Perhaps you have seen it? 1

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2. In an article “Drug Tests for Jobs Spreads, Raises Questions”, the St Augustine Record quotes a Miami drug testing consultant as saying “Testing of prospective employees for drug use has become so prevalent that detectable users may soon ﬁnd it impossible to get work.” Proponents of the procedure point to the improvement in worker eﬃciency and the reduction of absenteeism, accidents and theft that can be achieved by eliminating drug users from the work force. Opponents claim that the procedure is creating a class of unhireables and that some persons may be placed
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## This note was uploaded on 09/06/2009 for the course ENGRD 2700 taught by Professor Staff during the Spring '05 term at Cornell.

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practice_final_s09 - Engineering Statistics ENGRD2700...

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