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Date Created: 10/28/15
DIT 2010 Business Statistics Prof MW Varano Problem Set Study Guide 1 Spring 2009 Due TBA Notes 1 The purpose of this short problem set is to verify that the student has a basic understanding of descriptive statistics and basic probability 2 This problem set may be done individually or in groups of up to three students If you complete it as a group handin a single problem set containing the names of the group members Your choice of approach individually or in a group for this problem set does NOT commit you to use the same approach for future problem sets 3 The Empirical Rule referenced in the text is appropriate when the data follow a normal or hell shaped distribution Otherwise it shouldn t be used we established another rule yes that was a hint 4 Software especially Excel is of course useful in calculating descriptive statistics You may use software to solve these problems but this is not meant to be a computer exercise I ve deliberately chosen problems with very small data sets so that it s fairly easy to work problems out by quotpencil and paper quot which allows you to see exactly how the calculations are done Computers will be used more extensively as the size of the data sets grows and the calculations become more complex If you do use software or a calculator function to solve a problem make a note of that on your solution 5 Show all work necessary to obtain an answer Although it39s not required to word process the results it is highly recommended at the very least please handin a neat and well organized solution paper Problems NOTE for multiple choice questions CIRCLE the letter of your response and WRITE that letter in the space provided i 1 Which of the following statistics is NOT a measure of central tendency A arithmetic mean B median C mode D Q3 2 Which of the arithmetic mean median mode and geometric mean are resistant measures of central tendency A the arithmetic mean and median only B the median only C the mode and geometric mean only D the arithmetic mean and mode only ii In a rightskewed distribution A the median equals the arithmetic mean B the median is less than the arithmetic mean C the median is larger than the arithmetic mean D none of the above ii4 Which descriptive summary measures are considered to be resistant statistics A the arithmetic mean and standard deviation B the interquartile range and range C the mode and variance D the median and interquartile range iiS In rightskewed distributions which of the following is the correct statement A The distance from Q1 to Q2 is larger than the distance from Q2 to Q3 B The distance from Q1 to Q2 is smaller than the distance from Q2 to Q3 C The arithmetic mean is smaller than the median D The mode is larger than the arithmetic mean ii6According to the Chebyshev rule at least 9375 of all observations in any data set are contained within a distance of how many standard deviations around the mean C 3 B 2 D 4 I A bank branch manager interested in waiting times of customers A random sample of 12 customers is selected and yielded the following times in minutes 590 966 579 802 873 801 1049 835 668 564 547 991 a Find values for the following descriptive statistics the mean the median the standard deviation b What percentage of the observations are actually larger than the third quartile NOTE Compute the third quartile using the method of medians c What percentage of the observations are actually larger than the third quartile NOTE Compute the third quartile using the MS EXCEL Health care issues are receiving a great deal of attention in both academic and political arenas A sociologist recently conducted a survey of citizens over 60 years of age whose net worth is too high to qualify for Medicaid and have no private health insurance The ages of 25 uninsured senior citizens were as follows 0 61 62 63 64 65 66 68 68 69 70 73 73 74 75 76 76 81 81 82 86 87 89 90 92 a Find the arithmetic mean age of the uninsured senior citizens to the nearest hundredth of a year 7 7 b Identify the median age of the uninsured senior citizens if if c Find the third quartile using MS EXCEL of the ages of the uninsured senior citizens d Find the interquartile range of the ages of the uninsured senior citizens 7777 What shape does the distribution of the sample appear to have 7 77 Find the standard deviation of the ages of the uninsured senior citizens correct to the nearest hundredth of a year if AA 93 111 An economics professor uses the following grading system it consists of a nal grade on homework two midterm examinations and a nal examination The homework counts 10 toward the nal grade while each midterm examination counts 25 The remaining portion consists of the nal examination A student scored 95 in homework 70 on the rst midterm examination 96 on the second midterm examination and 72 on the nal The nal course average for this student is if g Identify which of the following is the correct statement 7 7 7 A Exactly one fourth of the senior citizens sampled are below 64 years of age B The middle 50 of the senior citizens sampled are between 655 and 730 years of age C Approximately 25 of the senior citizens sampled are older than 81 years of age D All of the above are correct One goal of management is to earn as much as possible relative to the capital invested One measure of success is return on equitythe ratio of net income to stockholder s equity Shown here are return on equity percentages for 25 companies Standard amp Poor 3 Stock Reports November 1997 90 190 229 416 114 158 527 173 123 51 173 311 96 86 112 128 122 145 92 166 50 303 147 192 62 a Compute the venumber summary for these data with labels for each response b Construct a boxwhisker plot neatly and with appropriate labels show plot in space below c Describe the shape and how you determined your conclusion Answer in space below A company produces a lightweight valve that is speci ed to weigh 1465 grams g Because of imperfections in the manufacturing process not all of the valves produced weigh exactly 1465 g In fact the weights of the valves produced are approx bellshaped ie normally distributed with a mean weight of 1465 grams and a standard deviation of 284 grams a Within what range of weights would approximately 95 of the valve weights fall b Approximately 16 of the weights are more than what value c Approximately 015 of the weights would be less than what value VI A random sample of 50 users of commercial Internet Service Providers ISP in August 2000 yielded the following monthly fees paid in dollars If needed use a stretched stemandleaf 20 40 22 22 21212010 20 20 201318 50 201815 8 22 25 2210 20 22 22 2115 23 3012 9 20 40 22 291915 20 20 20 201519 2114 22 2135 20 22 a Show a stemandleaf plot b Describe any shape location and spread patterns you see in the data c Comment on how much the larger in terms of customers were charging in August 2000 eg America Online etc d Which members in the sample may have been early adopters of fast access via cable modems or DSL lines VII Management at the ABC Company made a proposal to all of its sales representatives in different sales regions Questionnaires were sent to each representative The results are summarized below REGION OPINION I I East I Midwest I West I Total I Opposed 90 40 20 150 Not Opposed 30 60 10 100 120 100 30 a What is the probability that a questionnaire selected at random is that of a West region sales representative b What is the probability that the respondent is from the West region given that the response is favorable to the proposal c Are the events WEST region and OPPOSED independent events In either case yes or no show work to support your reasoning d What is the probability that the respondent is from the East or West region given that the response is favorable to the proposal e Are REGION and OPINION independent attributes YES or NO In either case yes or no show work to support your answer VIII The manager of a very large computer network developed the following probability distribution for the random variable X the number of interruptions per day Note The indicates that the printer malfunctioned l0 1 I2 I3 I a What is the probability 0f4 x 4 5 PX X I 03945 I 03920 I 03915 I 03912 I M I 03903 I interruptions the printer malfunctioned here b What is the probability of at most 1 interruption per day c What is the expected number of interruptions per day d Compute the standard deviation IX Consider the PriceEamings data set in your textbook or on the handout a Show a table that compares the actual percentage of observations in the intervals with those given by the Empirical Rule For example Intervals Actual 0o in Sample If Bell Shaped Normal b Show a printout of the standardized values for this data Hint use MS Excel s standardizexvalue mean stdev for the colunm of data c Identify extreme values in the data set using the following criterion Within 2 standard deviations not unusual Beyond 2 standard deviations unusual Beyond 3 standard deviations outlier Beyond 4 standard deviations extreme outlier d Create a box whisker plot for the data and comment on any ndings e Optional the inner fences in a boxwhisker plot are de ned as follows Q1 715 IQR and Q3 15 IQR Compute the inner fences for this data set f Optional Data outside the limits Q1 715 IQR and Q3 15 IQR are labeled as unusual Do there appear to be any for this data How would this information be help ll to a nancial analyst Data outside the limits Q1 730 IQR and Q3 30 IQR are labeled as outliers Are there any outliers
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