Posted: November 5th, 2015
Statistics
Follow all instructions carefully in presenting your answers. Be sure to show all your working. (Hand written responses are fine.)You will not need SPSS forquestions1-3.Forquestion4,please downloadthehousingdataset(fromLatte),then import it in to SPSS for analysis.
1) JetBlueAirlinesexaminedthebagsof80passengersandfoundthat20%ofthebagswere overweight.
a) Basedonthissample,whatisthe95%confidenceintervalfortheproportionofbagsthatare overweight? [6points]
b) Whatistheminimumsamplesizetheairlinewouldneedtoestimatewith95%confidenceto obtain a margin of error of +/- 3% for this estimate of the percentage of overweight bags? [6 points]
2) Afactoryrecentlytookasampletoassessthequalityofitscandyoutput,lookingatthreedifferent types of candy, and how many of each type of candy were damaged during the manufacturing process:
Candy #damaged Total # candiescounted
Apple hardcandy 15 50
Chocolatechew 18 50
Nutcluster 30 100
Thefactorymanagementwouldliketodeterminewhethertheproportionofcandythatisdamagedis different for these three types ofcandy.
a) Construct a contingency table for these data. [2points]
b) Istheproportionofcandythatisdamageddifferentforthesethreetypesofcandy?(Calculatethe appropriatestatistic,givethep-value,andstateyourconclusion.)[6points]
3) A manufacturer of headphones is interested in the sales of a particular headphone model in its stores in 8 airports. Some of these stores are located on the West and some on the East coast of the U.S. Also, the manufacturer recently conducted an advertising campaign. The sales before and after the advertisingcampaign,whichitraninFebruaryusingbillboardsintheairports,areshownbelow(i.e., dataforsalesinthosestoresinJanuaryanddataforsalesinthesamestoresforMarch.)
(Somedescriptivestatisticshavealsobeenprovidedinthetable.Youwillneedtodecidewhichones you need for your calculations in answering the questionsbelow.)
Store Location Sales inJan Sales inMarch Change insales
1 Eastcoast 195 230 35
2 Eastcoast 220 240 20
3 Eastcoast 220 250 30
4 Eastcoast 245 265 20
5 Westcoast 130 157 27
6 Westcoast 130 140 10
7 Westcoast 80 99 19
8 Westcoast 185 207 22
Summarystatistics
Allstores
Mean 175.63 198.50 22.88
SD 56.72 59.65 7.68
Eastcoast
Mean 220.00 246.25 26.25
SD 20.41 14.93 7.50
Westcoast
Mean 131.25 150.75 19.50
SD 42.89 44.71 7.14
Togetfullpointswhenansweringeachpartbelowbesureto:calculateanappropriatestatistic,statethe result of the test, and state yourconclusion.
a) Lookingatallthestores,isthereadifferenceinsalesbetweenJanuaryandMarch?[6points]
b) DidthecampaignhaveadifferenteffectonsalesforstoresontheEastcoastversusontheWest coast? [6points]
c) WasthereadifferenceinsalesinJanuaryforstoresontheEastcoastversusontheWestcoast? [6points]
4) Below are data for 40 houses located in one of two neighborhoods (A orB).
(This data is also provided in an Excel spreadsheet on the website for the class. Open the data in SPSSandconducttheanalysesrequiredtoanswerthequestions.Besuretopasteoutput(i.e.,tables) fromSPSSintoyouranswerswherethatisrequestedorelseyouwilllosepoints.)
Neighborhood AppraisedLand Value Appraised Valueof Improvements
SalePrice Has a yard?(yes/no)
A 56658 53806 255000 no
A 93200 11121 422000 no
A 76125 78172 290000 no
A 28996 5864 305900 no
A 30000 64831 118500 yes
A 30000 50765 93900 yes
A 46651 8573 191500 yes
A 45990 91402 184000 yes
A 42394 98181 168000 yes
A 47751 3351 169000 yes
A 63596 2182 208500 yes
A 51428 72451 264000 yes
A 54360 61934 237000 yes
A 65376 34458 286500 yes
A 42400 15046 202500 yes
A 40800 92606 168000 yes
A 12170 22786 375000 yes
A 24637 90598 169900 yes
A 30600 80858 135000 yes
A 44730 99047 176000 yes
B 38979 25946 140000 no
B 14861 59258 74900 no
B 14976 48957 57300 no
B 15244 55169 87500 no
B 18260 59267 82000 no
B 16680 55525 78000 no
B 53421 19792 175000 no
B 31417 99413 185000 no
B 32311 75343 123000 no
B 26817 78726 108000 no
B 24564 66533 108000 no
B 24564 71149 112900 no
B 27640 85347 106000 no
B 29656 78968 147500 no
B 13440 41177 61000 yes
B 45765 81227 320000 yes
B 16680 72867 99500 yes
B 17020 61935 93000 yes
B 25751 82259 110000 yes
B 25751 64568 100500 yes
a) Giveappropriatesummarystatistics(onemeasureofcentraltendencyandonemeasureof
variation)foreachofthe3variablesAppraisedLandValue,AppraisedValueofImprovements, and Sale Price, calculated separately for neighborhoods A and B. Important: PROVIDE ONLY ONE (APPROPRIATE) CENTRAL TENDENCY MEASURE AND ONE (APPROPRIATE) MEASUREOFVARIATIONFOREACHVARIABLEFOREACHNEIGHBORHOOD.[6
points]
b) Based on this data sample, do neighborhoods A and B differ in the number of houses with and withoutyards?Inyouranswerbesuretocalculateanappropriatestatistic,statetheresultofthe test,andstateyourconclusion.(PastetheoutputfromSPSSforthestatisticaltestthatyoudoin your answer, as well as stating your conclusion and writing out the appropriate statistic that supports your conclusion.) [6points]
c) Based on this data sample, do houses in neighborhoods A and B have different sale prices? (In youranswerbesuretocalculateanappropriatestatistic,statetheresultofthetestandstateyour conclusion.) (Paste the output from SPSS for the statistical test that you do in your answer, as well as stating your conclusion and writing out the appropriate statistic that supports your conclusion.) [6points]
d) Provide a correlation matrix for Appraised Land Value, Appraised Value of Improvements and SalePriceforneighborhoodBonly(youwillneedtosplitthedatatodothis–inSPSSunderthe Data menu use the “split file” command, split by neighborhood, and select “organize output by groups”). In words, explain the meaning of the correlation between Sale price and Appraised Land Value and the meaning of the correlation between Appraised Land Value and Appraised Value of Improvements. [6points]
Note:makesureyoudeselect”splitfile”afterdoingthisquestionpart,sothatyouanalyzingall the cases for the next twoparts.
e) Imagine you are interested in the relationship between house Sale price and Appraised Land Value while controlling for any effects of Appraised Value of Improvements. Conduct a linear regression that allows you to test this relationship (using data for all the houses, i.e., from both neighborhoods). State your conclusion about the relationship, and provide the statistics that supportyourconclusion.(PasteyourSPSSoutputforthisregressionintoyouranswer.)[6points]
f) ImagineyouareinterestedintherelationshipbetweenhouseSalepriceandNeighborhood,while controlling for any effects of Appraised Land Value and Appraised Value of Improvements on Sale price. Conduct a linear regression that allows you to test this relationship. State your conclusion about the relationship, and provide the statistics that support your conclusion. (Paste your SPSS output for this regression into your answer.) [6points]
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