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# Statistical Methods STA 2023

VC

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This 3 page Class Notes was uploaded by Winnifred Macejkovic on Thursday October 29, 2015. The Class Notes belongs to STA 2023 at Valencia College taught by Patrick Murphy in Fall. Since its upload, it has received 13 views. For similar materials see /class/231202/sta-2023-valencia-college in Statistics at Valencia College.

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Date Created: 10/29/15

Side bv side boxplots hamsters and rabbits The manager of a pet store records the amount of food eaten for each hamster and rabbit in the store The information he obtains is represented in the sidebyside boxplot below Note that the pets in the store are the individuals the type of pet hamster rabbit etc is a categorical variable and the grams of food eaten is a quantitative variable Hamsters Rabbits 7 8 910111213141516171819202122 Grams of food eaten NOTE each bullet below represents distinct comparison contrast 0 Hamsters have three outliers two at the low end 8 grams and 85 grams and one at the high end 22 grams Rabbits have one outlier at the low end 7 grams 0 The Interquartile Ranges IQRs of both groups are about the same hamsters IQR is 175 15 25 grams rabbits IQR is 18 16 2 grams 0 Ifwe exclude the hamster that ate 22 grams then we can say that 25 of the rabbits ate more than any hamster Q3 for rabbits is the same as maXX for hamsters again excluding the high outlier for hamsters 0 The spread for hamsters is from 8 grams to 22 grams and the spread for rabbits is from 7 grams to 195 grams The range for hamsters is 22 8 14 grams which is just a little more than for rabbits 195 7 125 grams Ifwe don t include the outliers we see that the range is the same for rabbits 195 14 55 grams as it is for hamsters 18 125 55 grams 0 The median grams of food eaten by rabbits is the same for hamsters 17 grams however both Q1 and Q3 for rabbits are higher than Q1 and Q3 for hamsters respectively Also the rabbits minX and maXX are higher than the minX and maXX for hamsters respectively ignoring outliers otherwise the reverse is true 0 The distribution for hamsters is definitely skewed left whereas the distribution for rabbits is fairly symmetrical MampMs Activity Tasks 1 Calculate f7 numbers 2 Write f7 numbers in notebook 3 Write each f7 number on a separate PostIt Note 4 Guess what p is 5 Place PostIt Notes on the whiteboard Questions Assume n 25 for calculations 20 of the Milk Chocolate MampMs in the world are orange so p 020 1 What is the area under the normal curve between 012 and 028 2 What percent of sample packets have a proportion of orange MampMs between 012 and 028 w 39 n tween 4 and 36 orange MampMs 4 5 What is the probability of opening a sample packet of MampMs and have more than 50 of them be orange 39 V L39 H 139ij 3 92 ll 6 What sample proportion of orange MampMs do Ineed to have to be in the top 1 of all saml NOTES Sampling Distributions n sample size 9 sample mean average of a quantitative variable describing a SAMPLE u population mean average of a quantitative variable describing the POPULATION f7 proportion of the SAMPLE with trait number of individuals in the SAMPLE which have trait n p proportion of the POPULATION with trait number of individuals in the POPULATION which have trait populationsize Statistic a number which describes a sample Examples x Sx 7 Parameter a number which describes a population Examples u 039 p Sampling Distribution The sampling distribution of a statistic is the distribution of values taken by the statistic in all possible samples of the same size from the same popu ation Unbiased Estimator A statistic used to estimate a parameter is unbiased if the mean of its sampling distribution is equal to the true value of the parameter being estimated Example p Example 0 u NOTES zscores for distributions In general the zscore for a value in a sampling distribution is the value minus the mean of the distribution value mean div1ded by the standard dev1ation of the distribution In notation This concept is stande dev1at10n the origin for the different sampling distribution zscore formulas seen in the table below Distribution zscore Z39Score With replaced formulas x w x 0 a A 75 x SDGC j W SD03

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