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# Statistical Methods BA 578

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This 4 page Class Notes was uploaded by Mose Rogahn on Friday October 30, 2015. The Class Notes belongs to BA 578 at Texas A&M University - Commerce taught by Edgar Manton in Fall. Since its upload, it has received 22 views. For similar materials see /class/232414/ba-578-texas-a-m-university-commerce in Business Administration at Texas A&M University - Commerce.

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Date Created: 10/30/15

Chapter 01 An Introduction to Business Statistics CHAPTER l An Introduction to Business Statistics A population is a set of existing units Consumers utilizing a particular product Any characteristic of a population unit is called a variable Quantitative values on the real number line Qualitative record unit into categories a Quantitative dollar amounts correspond to values on the real number line b Quantitative net pro t is a dollar amount c Qualitative which stock exchange is a category d Quantitative national debt is a dollar amount e Qualitative media is categorized into radio television or print Census examine all of the population units Sample subset of the units in a population a Descriptive statistics science of describing the important aspects of a set of measurements b Statistical inference science of using a sample of measurements to make generalizations about the important aspects of a population of measurements c Random sample selected in a manner so that on each selection from the population every unit remaining in the population on that selection has the same chance of being chosen d Systematic sample select every nth unit of a population Choosing the sample Without replacement guarantees that all of the units in the sample will be different units From Table 11 starting in the upper lefthand corner we obtain the following 2digit random numbers 33 03 92 85 08 5160 94 58 0914 74 24 87 07 Crossing out numbers greater than 27 because there are only 27 companies the sample consists of rms 03 08 09 14 and 07 That is 03 CocaCola 07 Sara Lee 08 CocaCola Enterprises 09 Reynolds American 14 Pepsi Bottling Group Chapter 01 An Introduction to Business Statistics From Table 11 starting in the upper righthand corner we obtain the following 2digit random numbers 88 22 52 68 0719 57 5149 0412 92 5110 Crossing out numbers greater than 30 because there are only 30 companies listed the sample consists ofindustries 22 07 19 04 and 10 That is 22 Toyota Motor 04 Continental Airlines 07 General Electric 10 Illinois Tool Works 19 Qualcomm a From Table 11 starting in the upper lefthand comer we obtain 5digit random num ers 33276 03427 92731 85689 08178 51259 60268 94904 58586 09998 14346 14403 24200 83308 07351 Crossing out the numbers greater than 73219 because there are only 73219 registration cards the rst ten registration cards in the sample are cards 33276 03427 08178 51259 60268 58586 09998 14346 24200 07351 b Most of the scores would fall between 36 and 48 because 36 is the smallest score in the sample and 48 is the largest score in the sample An estimate of the proportion of scores that would be at least 42 is 4665 0708 because 46 ofthe 65 sample scores are at least 42 Most waiting times will be from 4 to 116 minutes An estimate of the proportion of waiting times less than 6 minutes is found by counting the number of customers with waiting times 60 less than 6 minutes and dividing by the total of 100 customers m a People who oppose TV seX and violence would be most likely to respond Yes almost all respondents are concerned about seX language and violence b It is doubtful that a random sample would give the same results Given the number of people who watch shows containing seX vulgar language and violence it is doubtful that 96 to 97 percent of the population is concerned about seX language and violence on TV c It is highly doubtful that 90 of the general population desires a Vchip a Plot is in statistical control center can be represented by a horizontal line and spread around the line remains constant over time b Basing the limits on the minimum and maximum temperatures observed the lower limit is 152 degrees and the upper limit is 170 degrees Chapter 01 An Introduction to Business Statistics 113 a Yes in control There is constant variation at a horizontal level b Most breaking strengths will be between 468 lbs and 54 lbs Yes the waiting times are in control There is reasonably constant variation at a horizontal level A ratio variable is a quantitative variable measured on a scale such that ratios of values of the variables are meaningful and there is an inherently de ned zero value An interval variable is a quantitative variable such that ratios of values of the variable are not meaningful and there is not an inherently de ned zero value An ordinal variable is a qualitative variable such that there is a meaningful ordering or ranking of the categories A nominative variable is a qualitative variable such that there is no meaningful ordering or ranking of the categories Ordinal nominative ordinal nominative ordinal and nominative Nominative ordinal ordinal ordinal nominative and nominative When the population consists of two or more groups that differ with respect to the variable of interest Strata are nonoverlapping groups of similar units Strata should be chosen so that the units in each strata are similar on some characteristic often a categorical variable Cluster sampling is often used when selecting a sample from a large geographical region Because at each stage we cluster units into subpopulations First divide 1853 by 100 and round down to 18 We randomly select 1 company from the rst 18 in a list of all the companies From the company selected we simply count down 18 to get to the neXt company to select We continue this process until we have reached a sample size of 100 A strati ed random sample is selected by dividing the population into some number of strata and then randomly sampling inside each strata Potential strata students who live off campus and students who live on campus List all cities with population gt 10000 In each city randomly select a number of city blocks In each city block take a random sample of individuals The response variable is whether or not the person has cancer The factors or independent variables are age seX occupation and number of cigarettes smoked per day This is an observational study Chapter 01 An Introduction to Business Statistics 125 Undercoverageiwhen some groups in the population are left out of the process of choosing the sample Nonresponseino data obtained from a unit selected in a sample Response biasiwhen a sampling procedure systematically favors certain outcomes Sample may be biased because it is not stated that the recipients of the survey were chosen at random In addition there may be errors of undercoverage and nonresponse Voluntary response surveys usually give bias results Percentage of population that opposes the law probably lt 78 His cements are justi ed because voluntary response surveys are usually biased Using Table 11 and starting in column 3 we get the following random numbers 3693352131619 0414 06 30 253800 Numbering the companies from 00 to 34 this process yields a random sample of size 10 The process is not in statistical control and the higher percentages of people waiting too long occur early in the week A potential solution is to staff at a higher level early in the week Basic cable rates are increasing in a linear fashion on an annual basis Yes Pre71959 level of wins appears higher than post71959 level of wins

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