STATISTICAL METHODS INFORMATION ON THE FIRST MIDTERM EXAMINATION Date September 22 2010 Wednesday Time 9 15 10 20 Place SCI 3550 Examination Type Closed notes and books But you will be allowed to use one sheet of paper information sheet with the formulas and facts that you need This sheet should not have solutions of problems or examples Coverage Chapter 1 3 The important topics that you should know for the exam Chp 1 Statistics 1 1 1 2 Definition of statistics Types of Statistical Applications descriptive and inferential statistics 1 3 Elements of Statistics population variable sample statistical inference reliability of the inference 1 4 Types of Data Qualitative Quantitative nominal ordinal interval ratio data 1 5 Collecting Data Chp 2 Descriptive Statistics 2 1 Describing Qualitative Data 2 2 Graphical methods for quantitative data Stem and leaf displays and its interpretation Histograms and its interpretation 2 3 2 4 Measures of Central Tendency sample mean and population mean How to find mean How to find median position and depth of the median How to find mode unimodal bimodal multimodal 2 5 Measures of variability Why do we need a measure of dispersion sample range sample mean absolute deviation sample variance sample standard deviation why do we need sample standard deviation 2 6 Interpreting and Understanding standard deviation Chebyshev s Theorem for all distributions Emprical Rule for normally distributed data Given mean and standard deviation find the proportion of observations between two values find the limits given the percentages 2 7 Measures of relative standing position Percentiles Quartiles z scores how to find z scores use of z scores interpretation of z scores 2 8 Methods of Detecting Outliers Boxplots IQR QU QL Construction of the boxplots by using lowest value lower quartile median upper quartile highest value Interpretation of single and side by side boxplots Chp 3 Probability 3 1 Elements of Probability experiment simple event sample space event steps for calculating event probabilities 3 2 3 4 Compound events unions and intersections 3 3 Complementary events How to find the probability of a complement of an event 3 5 Conditional probability the Bayes rule 3 6 Probabilities of Unions and intersections additive rule multiplicative rule mutually exclusive events independent events showing whether two events are mutually exclusive or independent and given mutually exclusiveness and independents finding compound event probabilities 3 7 Random Sampling 3 8 Some Counting Rules STUDY QUESTIONS 1 Here is the number of home runs that Babe Ruth and Roger Maris hit during the years that they were with the New York Yankees BABE RUTH 54 59 35 41 46 25 47 60 54 46 49 46 41 34 ROGER MARIS 8 13 14 16 23 26 28 33 39 61 Note that Ruth s record of 60 home runs in one season was broken by another Yankee Roger Maris who hit 61 home runs in 1961 a What is the variable of interest Is this data qualitative or quantitative b Produce a back to back stem and leaf display for the home runs of Babe Ruth and Roger Maris and interpret Who was superior as a home run hitter c Construct boxplot for the home runs of Babe Ruth and interpret it 2 a A survey of local companies found that the mean amount of travel allowance for executives was 0 25 per mile The standard deviation was 0 02 Using the Chepyshev s theorem find the minimum percentage of the data values that will fall between 0 20 and 0 30 22 b The distribution of amounts spent per month for rent by students attending Computer University is mound shaped The mean monthly rental is 450 and the standard deviation is 125 approximately what percentage of rentals is between 75 and 825 3 The security manager of a large building reports that the probability is 0 05 that a fire alarm will not operate when needed Suppose that there are 3 alarms in the building and whether one operates or not does not affect the operation of others a What is the probability that all of them will operate during a particular fire b What is the probability that at least 1 will operate during a particular fire 4 At a large factory 89 employees were surveyed and classified according to their level of education and whether or not they smoked The data are shown in the table Educational level Not high school graduate Smoking Habits High school graduate College graduate Smoke 6 14 19 Do not smoke 18 7 25 A If an employee is selected at random find these probabilities a the employee is a high school graduate and smokes b the employee smokes given that s he graduated from college c given that the employee smokes s he is a college graduate B d Are the events smoke and not high school graduate independent Please justify your answer 5 A pregnancy test is 98 accurate in detecting pregnancy That is if a woman is pregnant it will show positive 98 of the time and show negative 2 of the time Furthermore if a woman is not pregnant it will show negative 98 of the time and positive 2 of the time Assume that there is a 50 probability that a woman who uses the test is pregnant a Find the probability that the test will be negative b Find the probability that if the test shows positive the woman is nor pregnant 6 Consider the following system of components connected as in the accompanying pictures The probability of failure for components in the system is 0 1 Assume components operate independently of each other 2 INPUT 1 OUTPUT SUBSYSTEM A 3 SUBSYSTEM B a Find the probability that the system will fail to operate properly b Find the probability that at lease one of the subsystems will fail