Popular in Statistics for Biosciences
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This 3 page Class Notes was uploaded by Baki Moore on Wednesday September 30, 2015. The Class Notes belongs to STP 231 at Arizona State University taught by in Fall 2015. Since its upload, it has received 101 views. For similar materials see Statistics for Biosciences in Statistics at Arizona State University.
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Date Created: 09/30/15
Example Due to decreasing revenue and economic conditions many states have tried to legalize gambling or in states where gambling is already legal expand casino operations To measure public opinion in Kansas a random sample of residents was selected and each response was categorized according to revenue preference and age The results are given in the following contingency table m Liquor Stores Elm 68 12 1820 33 113 2130 55 121 50 226 3144 117 109 132 358 At least 45 158 110 90 358 Total 363 408 284 1055 Example Continued a What is the probability the resident is in favor of legalized gambling b Suppose the person is in favor of stateowned liquor stores What is the probability the person is 3144 years old c What is the probability the resident is 2130 years old and in favor of some other option d What is the probability the resident selected is 1820 or at least 45 years old e Are the events favoring liquor stores and 3144 independent Explain Solution 0 G Favor gambling o L Favor liquor store 0 OP Favor other options aPG3631055O34 bP3144 LP3144 amp LPL109408O27 cP21 30 amp OP501055005 dP18 20 or at least 45P18 20Pat least 45P18 20 amp at least 45 l P18 20Pat least 45 11310553581055O45 Example for you to try o In a study of heart disease in male federal employees researchers classified 356 volunteers according to their socioeconomic status SES and their smoking status The three categories of SES were Upper Middle and Lower Smokers were Current Former or Never Below is the table that summarizes the data 51 22 43 116 Current Former 92 21 28 141 Never 68 9 22 99 A Total 211 52 93 356 Example Continued 0 a Among upper class employees approximately what percentage are current smokers o b What percentage of the volunteers have never smoked and are in the lower class SES 0 c Suppose the employee is a former smoker What is the probability the employee is in the middle class SES 0 d What percentage of the volunteers are former smokers e Are upper class employees and current smokers independent I You do this on your own for practice Example 0 According to the Energy Information Administration 651 of all housing units have a ceiling fan 55 of all households have ceiling fans and are owned 426 of all housing units have a ceiling fan and are fully air conditioned Suppose a household is randomly selected 0 a Given the household has a ceiling fan what is the probability it is owned 0 b If the household has a ceiling fan what is the probability it is fully air condMoned o c Suppose having a ceiling fan and being fully air conditioned are independent events What is the probability the household has a ceiling fan or is fully air conditioned Solution 0 Define events 0 C Room has ceiling fan 0 W Room is owned 0 A Room has air conditioner o PCO651 PC amp WO55 and PC ampAO426 o a Find Pw C Pw CPC amp WPCO55O651O84 o b Find PAI C PAl CPC amp APCO426O651206543779 Solution Continued 0 c PC orAPCPAPC ampA 0 Since A and C are independent we have I PC amp APCgtltPA 0 Next recall we are given PC ampAO426 and PCO651 then PAPC amp APCO426O651O6543779 0 Finally we substitute values into our original equation I PC orAPCPAPC ampA o 0651O6543779O426 0 208794
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