week 2: introductory definitions
week 2: introductory definitions MAT117
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This 5 page Class Notes was uploaded by WB on Sunday September 20, 2015. The Class Notes belongs to MAT117 at Pace University taught by Dr. Glenn Miller in Fall 2015. Since its upload, it has received 76 views. For similar materials see Elementary statistics in Mathematics (M) at Pace University.
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Date Created: 09/20/15
Date 942015 Fri Introductory definitions Population the set of all individuals under consideration Parameter a numerical characteristic of a population Sample a subset of a population Statistic a numerical characteristic of a sample One goal of statistics Use the statistic computed from the sample to estimate the value of the parameter of the population EX An economist needs to find the unemployment rate in the NYC region She surveys 3000 New Yorkers and finds that 180 of them are currently unemployed Find the population parameter sample and statistic up Population all members of the NYC region workforce quotthose who are willing and able to workquot Parameter the percent of all members of the NYC region workforce who are currently unemployed Sample 3000 members of the NYC workforce Statistic 6 of the 3000 members of the NYC workforce are currently unemployed Notice 1 3000 is the sample size Sample size will be consistently denoted as n in this course And the size of the population will be denoted as N So here n3000 Napproximately 8 million 2 Parameter is a generalization of the statistic a value ex A mean or a proportion one would obtain if it were possible to find the value of the variable being studied for all individuals in the population Type of data Consider the data as it is collected by the researcher from each individual in the sample Qualitative Type of data Discrete can be counted Quantitative Continuous can be measured to any degree of accuracy Qualitative data An attribute Ex A surveyor asks which candidate you are likely to vote for Quantitative data Numerical More examples 1 You work for the research and development division of a major pharmaceutical company The company has developed a new diet drug and your boss has asked you to test the drug s effectiveness You design a study in which a group of 642 overweight people will be randomly assigned to two equal subgroups one group of 321 will be given the new diet drug and the other group of 321 will be given a placebo a pill that contains no medication For the group given the diet drug the average weight loss over a threeweek period was 12 lbs For the group given the placebo the average weight loss over the same time period was 5 lbs Population all overweight people Parameter average weight loss for all overweight people who are treated with the drug and average weight loss for all overweight people who are given the placebo 321 overweight people given the diet drug and the other group of 321 people given a placebo Statistic for the people given the diet drug the average weight loss over a three week period was 12 lbs For the group given the placebo the average weight loss over the same time period was 5 lbs Type of data continuous how much weight did you lose 2 You are the head actuary in the Automobile Insurance division of a large insurance company The company s president wants a report from you to investigate if drivers who talk on cellular phones in their car have more accidents than those who never talk on cell phones while driving You survey 3245 randomly chosen drivers and find that 560 of those drivers use a cell phone while they drive while the other 2685 drivers do not 125 of the drivers with cell phones had accidents in the last three years while 550 of the drivers without phones had accidents in the last three years Population all drivers who text and all drivers who do not text Parameter proportion of all texting drivers who have accidents and proportion of all nontexting drivers who have accidents 560 drivers with cell phones and 2685 drivers who do not text Statistic if 223 of the texting drivers had accidents and 205 of non texting phone drivers had accidents Type of data qualitative did you have an accident 3 You are a chief auditor at an accounting firm A Fortune 500 company reports accounts receivables money owed to the company for services rendered of 7500000 There are 3450 different entities that owe money to the company Some of these entities will not be able to pay the debts they have incurred Your job is to estimate the percentage of the accounts receivable that should be written off as doubtful accountsquot You conduct a thorough check on 225 of the entities and determine that approximately 28 will be unable to meet their obligation to your client Population all 3450 entities that owe money to the company Parameter proportion of all entities that will be unable to meet their obligation to the company 225 entities that owe money to the company Statistic 85 2 124 of the 225 entities sampled will be unable to meet their financial obligation to the company Type of data qualitative will you be able to pay 4 In 1954 400000 children participated in a study of the effectiveness of the Salk vaccine for polio Half of the children received the vaccine while the other half was given a harmless salt solution Only 50 of the children who received the vaccine contracted polio while 150 of the children who were given the salt solution contracted the disease Population all children in the world Parameter proportion of all children who will contract polio after being vaccinated and proportion of all children who will contract polio when given only the placebo 200000 children who were vaccinated and 200000 children who were given placebo 50 200000 Statistic 0025 of the vaccinated children contracted polio and 150 200000 0075 of children given placebo contracted polio Type of data qualitative did you contract polio 5 A survey of young doctors at a California medical school has found that of the women and E of the men believed they had been sexually harassed during training The study was based on a written survey of 133 interns and residents in internal medicine at the University of California at San Francisco Responses were received from 82 interns and residents 49 men and 33 VVOHQGH Population all interns and residents at medical schools Parameter proportion of all residents and interns who believe they have been sexually harassed 133 residents and interns Statistic of the 82 respondents E of the women and E of the men interns and residents sampled believed they had been sexually harassed during training Type of data qualitative were you harassed 6 A market research company studied the daily activities of 3000 people who were chosen from telephone and voter registration lists to re ect the national population including people aged from 18 to 90 in all parts of the country and economic classes The study found that Americans spend an average of 7 hours and 25 minutes sleeping an average of 4 hours and 44 minutes on work related activity 4 hours and 23 minutes for entertainment and food related activities accounted for 2 hours and 7 minutes per day Population all adults ages 18 to 90 in the US Parameter Average amount of time all adults spend sleeping working etc 3000 US adults Statistic The study found that 3000 Americans spend an average of 7 hours and 25 minutes sleeping an average of 4 hours and 44 minutes on work related activity 4 hours and 23 minutes for entertainment and food related activities accounted for 2 hours and 7 minutes per day Type of data Continuous time is measured
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