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##### UMUC STAT 230 Final Exam Spring 2013

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Question;STAT;230 Final Exam;UMUC;Spring;2013;100;Points;---------------------------------------------------------------------------------------------------------------------;Use;the information below to answer Questions 1 through 4.;Given;a sample size of 36, with sample mean 670.3 and sample standard deviation 114.9;we perform the following hypothesis test.;Null;Hypothesis;Alternative;Hypothesis;1. What;is the test statistic?;2. At;a 10% significance level (90% confidence level), what is the critical value in;this test? Do we reject the null;hypothesis?;3. What;are the border values between acceptance and rejection of this hypothesis?;4. What;is the power of this test if the assumed true mean were 710 instead of 700?;Questions;5 through 8 involve rolling of dice.;5. Given;a fair, six-sided die, what is the probability of rolling the die twice and;getting a ?1? each time?;6. What;is the probability of getting a ?1? on the second roll when you get a ?1? on;the first roll?;7. The;House managed to load the die in such a way that the faces ?2? and ?4? show up;twice as frequently as all other faces.;Meanwhile, all the other faces still show up with equal frequency. What is the probability of getting a ?1? when;rolling this loaded die?;8. Write;the probability distribution for this loaded die, showing each outcome and its;probability. Also plot a histogram to;show the probability distribution.;Use;the data in the table to answer Questions 9 through 11.;x;3;1;4;4;5;y;1;-2;3;5;9;9. Determine;SSxx, SSxy, and SSyy.;10. Find;the equation of the regression line.;What is the predicted value when;11. Is;the correlation significant at 1% significance level (99% confidence level)? Why or why not?;Use;the data below to answer Questions 12 through 14.;A;group of students from three universities were asked to pick their favorite;college sport to attend of their choice;The results, in number of students, are listed as follows;Football;Basketball;Soccer;Total;Maryland;60;70;20;150;Duke;10;75;15;100;UCLA;35;65;25;125;Total;105;210;60;375;Supposed;a student is randomly selected from the group mentioned above.;12. What;is the probability that the student is from UCLA or chooses football?;13. What;is the probability that the student is from Duke, given that the student;chooses basketball?;14. What;is the probability that the student is fromMaryland and chooses soccer?;Use;the information below to answer Questions 15 and 17.;There;are 3600 apples in a shipment. The;weight of the apples in this shipment is normally distributed. It is found that it a mean weight of 14;ounces with a standard deviation of 2.5 ounces.;15. How;many of apples have weights between 13 ounces and 15 ounces?;16. What;is the probability that a randomly selected mango weighs less than 12.5 ounces?;17. A;quality inspector randomly selected 100 apples from the shipment.;a. What;is the probability that the 100 randomly selected apples have a mean weight;less than 12.5 ounces?;b. Do;you come up with the same result in Question 16? Why or why not?;18. A;pharmaceutical company has developed a screening test for a rare disease that;afflicted 2% of the population.;Unfortunately, the reliability of this test is only 80%, which means;that 20% of the tested will get a false positive. If a subject is tested positive based on this;test, what is the probability that he has the disease?;Use the information below to answer;Questions 19 and 20.;Benford's law;also called thefirst-digit law, states that in lists of numbers from;many (but not all) real-life sources of data, the leading digit is distributed;in a specific, non-uniform way shown in the following table.;Leading;Digit;1;2;3;4;5;6;7;8;9;Distribution;of Leading Digit (%);30.1;17.6;12.5;9.7;7.9;6.7;5.8;5.1;4.6;The owner of a small business would like to audit;its account payable over the past year because of a suspicion of fraudulent;activities. He suspects that one of his;managers is issuing checks to non-existing vendors in order to pocket the;money. There have been 790 checks;written out to vendors by this manager.;The leading digits of these checks are listed as follow;Leading Digits;50;15;12;74;426;170;11;23;9;19. Suppose you are hired as a forensic accountant by;the owner of this small business, what statistical test would you employ to;determine if there is fraud committed in the issuing of checks? What is the test statistic in this case?;Hardness of Gem ? Questions 23 and 24;Listedbelow are measured hardness indices from three different collections of;gemstones.;Collection;Hardness Indices;A;9.3;9.3;9.3;8.6;8.7;9.3;9.3;--;---;---;---;---;---;9.91;0.10;B;8.7;7.7;7.7;8.7;8.2;9.0;7.4;7.0;---;---;---;---;---;8.03;0.60;C;7.2;7.9;6.8;7.4;6.5;6.6;6.7;6.5;6.5;7.1;6.7;5.5;7.3;6.82;0.34;You are also given that.;20. What;is the test statistic?;21. Use;a 5% significance level (95% confidence level) to test the claim that the;different collections have the same mean hardness.;22. A;couple has 3 daughters. The wife is;expecting another baby.;a. What;is the probability that the new baby is a girl again?;b. Suppose;the new baby turns out to be a girl. What;is the probability that a family with 4 children that are all girls?;Use;the data below to answer Questions 26 and 27.;This;is a summary of the midterm scores for two sections of STAT 230. The midterm questions and the grading;criteria are different in these two sections.;Section A;Student;Score;Section B;Student;Score;A;70;H;15;B;42;I;57;C;53;J;48;D;61;K;90;E;22;L;85;F;85;M;73;G;59;N;49;-----;------;O;39;23. What;are the mean and standard deviation of the scores in Section A?;24. We;notice that StudentF in Section A;and StudentL in Section B have the;same numerical score.;a.;How do they stand;relative to their own classes?;25. Peter;Paul, Mary, Andrew, John, and Martha are members of the pastoral council at a;local church. They are to be seated at;one side of a long conference table in a pastoral council meeting.;a. How;many possible ways can these 6 council members can be seated?;b. How;many possible sitting arrangements are there if only gender is considered in;the process?;26. A;banquet organizer knows that not all 600 invited guests will show up at an;event. Based on past experience, only;80% of the invited guest for this special event will come. When expensive dishes are served, it would be;prudent not to order the full 600 plates because a good number of them will be;wasted. On the other hand, the banquet;organizer will try to stay within 7% probability that he would not have to rush;to prepare the expensive dishes. How;many of these expensive dishes would you order if you were organizing this;banquet?

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