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## Prob&Stat Inference

by: Chelsie Cronin

127

0

3

# Prob&Stat Inference ECON 3640

Marketplace > University of Utah > Economcs > ECON 3640 > Prob Stat Inference
Chelsie Cronin
The U
GPA 3.81

Staff

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This 3 page Class Notes was uploaded by Chelsie Cronin on Monday October 26, 2015. The Class Notes belongs to ECON 3640 at University of Utah taught by Staff in Fall. Since its upload, it has received 127 views. For similar materials see /class/230032/econ-3640-university-of-utah in Economcs at University of Utah.

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Date Created: 10/26/15
Economics 3640001 Instructor Sanghoon Lee Lecture 3 Reading Assignment Ch2 Methods for Describing Sets of Data 26 N 27 Ex Active nuclear power plants p66 amp p71 The US Energy Information Administration monitors all nuclear power plants operating in the US The table below lists the number of active nuclear power plants operating in each ofa sample of 20 states State Number Of Power Plants a Find the mean median and mode of this data set Alumnu 5 3 b Eliminate the largest value from the data set and 4 5 repeat part a What effect does dropping this If measurement have on the measures of central tendency found in part a M i Miisiwmpi I c Arrange the 20 values in the table from lowest to Eur HHTPFM39K39 1 highest Next eliminate the lowest two values and Nrhygl lmn the highest two values from the data set and find Ohm V 2 the mean of the remaining data values The result is 7 called a 10 trimmed mean since it is calculated frunncswu 3 after remov1ng the highest 10 and the lowest 10 farmlm j of t e ata values What advantages does a ixcomm 3 trimmed mean have over the regular arithmetic mean d Find the variance and the standard deviation of the data set e Eliminate the largest value from the data set and repeat part d What effect does dropping this measurement have on the measures ofvariation found in part d f Eliminate the smallest and largest value from the data set and repeat part d What effect does dropping both of these measurements have on the measures ofvariation found in part d You now know that the S measures the variability of a set of data and how to calculate it The larger the S the more variable the data are The smaller the S the less variation in the data 26 Interpreting the Standard Deviation TABLE 22 EPA Mileage Ratings on 100 Cars In Table 22gt 7 3699 and S 242 421 375 37733457 JTS3941 If we examine the data we find that 68 of the 100 measurements are in the interval 5qu 3457 3773 to 3941 37 3 3 7 34x 381 3772s3215372s4l83 96 Table 27 The Empirical Rule applies to moundshaped and symmetric distributions of data a Approximately 68 of the measurements will fall within 1 standard deviation of the mean ie within the interval J 7 s J s for samples and u 7 039 u a for populations b Approximately 95 of the measurements will fall within 2 standard deviations of the mean ie within the interval J 7 2s J 2s for samples and u 7 2039 u 20 for populations c Approximately 997 essentially all of the measurements will fall within 3 standard deviations of the mean ie within the interval J 7 3s J 3s for samples and u 7 317 u 30 for populations Table 26 Chebyshev39s Rule applies to any data set d Generally for any number k greater than 1 at least 1 7 lkz of the measurements will fall within the interval J 7 ks J ks for samples and u 7 k0 u kg for populations Ex 284 The following is a sample of 25 measurements 76611891191087759107777912101086 a Compute J s2 and s for this sample b Count the number of measurements in the intervals J i s J i 2s and J i 3s Express each count as a percentage of the total number of measurements c Compare the percentages found in part b to the percentages given by the Empirical Rule and Chebyshev39s Rule Ex 285 Given a data set with a largest value of 760 and a smallest value of 135 what would you estimate the standard deviation to be Explain the logic behind the procedure you used to estimate the standard deviation Suppose the standard deviation is reported to be 25 Is this feasible Explain Ex 288 Recommendation letters for professors Recall that n 148 J 228 and s 148 a Sketch the relative frequency distribution for the number of recommendation letters included in each application for the experimental psychology position Assume the distribution is moundshaped and relatively symmetric b Locate an interval on the distribution part a that captures approximately 95 of the measurements in the sample c Locate an interval on the distribution part a that captures almost all the sample measurements 27 Numerical Measures of Relative Standing Def 213 The sample zscore for a measurementx is z x 7J s The population zscore for a measurement x is z x 7 u 7 Eg sample 2 710 x is 10 standard deviation below the sample mean Ex 2100 Compute the zscore corresponding to each of the following values of x ax40s5J30 ds4x20J30 The zscore re ects the relahve standsng of the measurement A large posrhve zscore 1mphes that the measurementrs largerthan almost all othermeasurements whereas alarge negahve zscore 1ndscates that the measurement 1s smaller that almost every other measurement lf azscore 1s 0 or near 0 the measurement 1s located at ornearthe mean ofthe sample orpopulahon Rclume lrcqutnu u 3 n In is pm as nan Measureme my 7 i j I alt The Empirical Rule can be rewntten a Approxrmately 68 of the measurements uull have azscore between 1 and l b Approxrmately 95 of the measurements uull have azscore between 2 andZ c Approxrmately 99 7 essenhally all of the measurements wrll have azscore between 3 and3 EX lel GPAs of students At one unrversrty the students are grven zscores at the end of each semester rather than the tradshonal GPAs The mean and standard deyratron of all students cumulahve GPAs on whsch thezscores are based are 2 7 and 5 respectrvely a Translate each ofthe follouungzscoresto conespondsng GPAscores 2010 525 b Students yuth zscores below 1 6 are put on probahon What 1s the conespondsng probatronary GPM cThepresrdentoltheum errt d L 16of39h 39d t 39h 39 quot the top 2 5 wrth mama cum lande honors Where approxrmately should the hmrts be set m terms of z scoresl In terms of GPAsl What assumphon 1f any dsd you make about the dsstnbuhon ofthe GPAs at the unrversrtyl

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