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# STAT 230 Final Exam

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Date Created: 11/06/15

STAT 230 Introductory Business Statistics Spring 2013 Final Exam 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 6703 and sample standard deviation 1149 we perform the following hypothesis test Null Hypothesis Ha u700 Alternative Hypothesis 1 What is the test statistic 6703700 114936 2971915 2 At a 10 significance level 90 confidence level what is the critical value in this test Do we reject the null hypothesis Table V value of 01 is 1645 1645 lt z gt1645 3 What are the border values between acceptance and rejection of this hypothesis Page 1 STAT 230 Introductory Business Statistics Exam 4 Spring 2013 Final 700 1645 100 36 700 1645 100166666 700 1645 600 700 987 70987 700 987 69013 What is the power of this test if the assumed true mean were 710 instead of 700 2L 70987 710 013 00013 21 0040 100 100 2U 69013 710 1987 01987 Zn 0753 100 100 0753 0040 0749 B 1 0749 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 What is the probability of getting a 1 on the second roll when you get a 1 on the first roll PAB PA PBA PB PBA PB I 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 P1P2P3P4P5P6 1 2X1X2X1X1X1X 1 Page 2 STAT 230 Introductory Business Statistics Spring 2013 Final Exam 8Xl 8 Write the probability distribution for this loaded die showing each outcome and its probability Also plot a histogram to show the probability distribution P1 1X 125 125 P2 2X 125 25 P3 1X 125 125 P4 2X 125 25 P5 1X 125 125 P6 1X 125 125 Probability Histogram 025 02 015 01 005 I P1 I P2 I P3 I P4 I P5 I P6 m Use the data in the table to answer Questions 9 through 11 x 3 l 4 4 5 y l 2 3 5 9 Page 3 STAT 230 Introductory Business Statistics Spring 2013 Final Exam 9 Determine SSxx SSxy and SS X Y XX quot2 yS quot2 X X y 5 3 1 3 28A2 04 138 A2784 328 138 056 2 1 228quot2 2304 1 38A2 784 228 138 2 3 428quot2 144 338 A2 64 428 338 12 4 5 428quot2 144 538 A2 144 428 538 20 9 528quot2 484 938 A2 2704 528 938 45 Total 14 19 308 448 7444 Mean 28 38 x24 10 Find the equation of the regression line What is the predicted value when Slope B SSXy SSXX 448 30 149 yintercept ymean B Xmean 38 149 28 38 417 What is the predicted value when x 4 037 1494 037 596 11 Is the correlation significant at 1 significance level 99 confidence level Why or why not Coefficient of correlation r SSXy sqrt SSXXX SSyy 448 sqrt 30 7744 Page 4 STAT 230 Introductory Business Statistics Spring 2013 Final Exam 448 42416 r Linear correlation t rsqrtn 2sqrt 1 r2 1056 sqrt l 2 sqrt l 10562 1056 1 8944 1056 8944 There appears to be some correlation nearly a direct opposition 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 PAUB PA PB PAm B PA UCLA 125375 03333 PB Football 105375 028 PA m B PAPB P333328 09333 PA PB PAm B 03333 028 09333 13 What is the probability that the student is from Duke given that the student chooses basketball PA B 75210 Page 5 STAT 230 Introductory Business Statistics Spring 2013 Final Exam 14 What is the probability that the student is from Maryland and chooses soccer 20375 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 25 ounces 15 How many of apples have weights between 13 ounces and 15 ounces PU3SXSl 21314 l 04 21514 1 04 25 25 1554 1554 3108 3108 3600 16 What is the probability that a randomly selected mango weighs less than 125 ounces P z lt 125 125 14 06 2257 25 6 2257 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 125 ounces SE 25sqrt 100 2510 P mean weight lt 125 125 14 025 l5025 Page 6 STAT 230 Introductory Business Statistics Spring 2013 Final Exam 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 af icted 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 Benford39s law also called the firstdigit 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 Distributio f n O 301 176 125 97 79 67 58 51 46 Leadlng Digit 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 Page 7 STAT 230 Introductory Business Statistics Spring 2013 Final Exam L d39 65a mg 50 15 12 74 426 170 11 23 9 Digits 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 Hypothesis Test 20 What is the critical value for this test at the 5 significance level 95 confidence level Do the data provide sufficient evidence to conclude that there is fraud committed Hypothesis Test versus Confidence Interval Questions 21 through 22 Two different simple random samples are drawn from two different populations The first sample consists of 20 people with 10 having a common attribute The second sample consists of 2000 people with 1404 of them having the same common attribute 21 Perform a hypothesis test of 191 192 with a 5 significance level 95 confidence level 22 Obtain a 95 confidence interval estimate of 191 192 Do you come up with the same conclusion for Question 21 Why or why not Hardness 0f Gem Questions 23 and 24 Listed below are measured hardness indices from three different collections of gemstones Page 8 STAT 230 Introductory Business Statistics Spring 2013 Final Exam Collection Hardness Indices 371 sf A 93 93 93 86 87 93 93 991 010 B 87 77 77 87 82 90 74 70 803 060 C 72 79 68 74 65 66 67 65 65 71 67 55 73 682 034 372799 You are also given that 23 What is the test statistic 2799 24 Use a 5 significance level 95 confidence level to test the claim that the different collections have the same mean hardness 25 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 A 70 B 42 C 53 D 61 E 22 Section B Student Score H 15 I 57 J 48 K 90 L 85 Page 9 STAT 230 Introductory Business Statistics Exam Spring 2013 Final F 85 M 73 G 59 N 49 o 39 26 What are the mean and standard deviation of the scores in Section A 704253612285597 I 7056A24256A25356quot26156A22256A28556A25956A2 71 14quot214quot23A25A234A229A23A2 6 19619692511568419 6 24326 4053333 l4053333 27 We notice that Student F in Section A and Student L in Section B have the same numerical score a How do they stand relative to their own classes Section B has a mean of 57 15574890857349398 57 1557quot25757A24857A29057quot28557quot273 57quot249 57A239 57A2 81 42A20A29A233A228quot216A28A218quot2 7 1764 0 81 1089 784 256 64 324 4362 7 43627 6231429 6231429 2496 Page 10 STAT 230 Introductory Business Statistics Exam x 5c85 56 Z b 28 29 Spring 2013 Final SCCtiOH A mean 5c 56 and its standard deviation S 2 2013 2144 s 2013 SCCtiOH B mean 5c 57 and its standard deviation S 2 243996 x 5c 90 57 132 S 2496 Which student performed better Explain your answer Composite sampling is a way to reduce laboratory testing costs A public health department is testing for possible fecal contamination in public swimming pools In this case water samples from 5 public swimming pools are combined for one single test and further testing is performed only if the combined sample shows fecal contamination Based on past experience there is a 3 chance of finding fecal contamination in a public swimming area What is the probability that a combined sample from 5 public swimming pools has fecal contamination 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 Page 11 STAT 230 Introductory Business Statistics Spring 2013 Final Exam Q n 654321 1 6 1 72 16 b How many possible sitting arrangements are there if only gender is considered in the process 30 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 PA PB PA B 8O7 13 82 07 93 Page 12

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