Posted: November 5th, 2015

Statistics

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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