Final Exam Review Questions Solutions Guide

Review Questions

Solutions Guide

You may want toPRINT THIS so you can carefully check your answers.  Be sure toask your instructor if you have questions about any of the solutions given below.

1.                  Determine if each of the following represents nominal, ordinal, interval, or ratio data.

a.                   Movie ratings

b.                  Test scores

c.                   Colors of shirts

2. Thefollowing numbersrepresenttheweights in poundsofsix 7- yearold childrenin Mrs.Jones'2ndgradeclass.

{25,60,51,47,49,45}

Findthemean;median;mode;range;variance;standard deviation.

3. Ifthevarianceis846,whatis thestandarddeviation?

4. Ifwe havethefollowing data

34,38,22,21,29,37,40,41,22,20,49,47,20,31,34,66

Drawastemandleaf.Discusstheshapeofthedistribution.

5.What type of sampling technique is (a) a wheat field is divided into sections and a random sample of stocks are taken from each section, and (b) a manufacturer measures every 80^th bottle to test for quality?

6.If a data set with a normal distribution has a mean of 32 and a standard deviation of 4.9, what percent of the data would you expect to find between 27.1 and 36.9?  What range encompasses 99.7% of these data?

7. Determine the regression equation for the following data:

            X:  4  5  7  3  2   7  8  9  7  6   4   6   5  9  3  2  1

            Y:  9  7  8  6  9   5  6  4  3  6   7   8   9  3  4  2  4

8.If the correlation coefficient is -.749, what would be the value of the coefficient of determination?

9. To predict theannualriceyield in poundsweusetheequation

yˆ=859+5.76x1+3.82x2,wherex1representsthenumberofacres plantedandwherex2representsthenumberofacres harvestedandwherer2= .94.

a)            Predicttheannualyield when3200acresareplantedand3000 areharvested.

b)           Interprettheresultsofthis r2value.

10. TheStudentServicesofficedidasurveyof500studentsin which theyaskedifthestudentis part-timeorfull-time.Anotherquestion askedwhetherthestudentwasatransferstudent.Theresultsfollow.

TransferNon-Transfer                                  Row Totals

Part-Time

100

110

210

Full-Time

170

120

290

Totals

270

230

500

a) Ifastudentis selectedatrandom(fromthis groupof500 students),findtheprobability thatthestudentis atransferstudent.P (Transfer)

b) Ifastudentis selectedatrandom(fromthis groupof500 students),findtheprobability thatthestudentis aparttimestudent. P (PartTime)

c)Ifastudentis selectedatrandom(fromthis groupof500 students),findtheprobability thatthestudentis atransferstudent andaparttimestudent.P(transferANDparttime).

d)Ifastudentis selectedatrandom(fromthis groupof500 students),findtheprobability thatthestudentis atransferstudentif we knowheis aparttimestudent.P(transfer| parttime).

e)Ifastudentis selectedatrandom(fromthis groupof500 students),findtheprobability thatthestudentis aparttimegivenhe is atransferstudent.P(parttime| transfer)

f)Aretheeventsparttimeandtransferindependent?Explain mathematically.

g)Aretheeventsparttimeandtransfermutuallyexclusive.Explain mathematically.

11. Ashipmentof40televisionsetscontains3defectiveunits.How manywayscanavendingcompanycanbuyfiveoftheseunits and receivenodefectiveunits?

12. In the US, 28% of people consider snickerdoodle as their favorite cookie.  You asked 5 people if their favorite cookie was snickerdoodle.  Create the probability distribution for the possible outcomes.

13. TherandomvariableX representstheannualsalariesin dollars of agroupofteachers.FindtheexpectedvalueE(X).

X = {$35,000;$45,000;$55,000} where,

P(35,000)= .4;P(45,000)= .3;P(55,000)= .3.

14. Anadvertisingagencyis hiredtointroduceanewproduct.The agencyclaims thatafterits campaign61%ofall consumersare familiarwith theproduct.Weask7randomlyselectedcustomers whetherornottheyarefamiliarwith theproduct.  (a) findtheprobability that,outof7 customers,exactly4arefamiliarwith theproduct; (b) find the probability that at least 3 customers are familiar with the product; and (c) find the probability that at most 5 are familiar with the product.

15. Themeannumberofcarsperminutegoing throughthe Eisenhowerturnpikeautomatictoll is about7.Findtheprobability that exactly3will gothroughin agivenminute.

16. Labelthefollowing ascontinuousordiscretedistributions.

a)         Thelengthsoffishin acertainlake.

b)         Thenumberoffishinacertainlake.

c)         Thediameterof15treesin aforest.

d)         How manytreesareonafarmer'sacre.

17. Onadrysurface,thebrakingdistance(in meters)ofacertaincar is anormaldistribution with µ = 45.1mandσ = 0.5

(a)          Findthebrakingdistancethatrepresentsthe91stpercentile.

(b)         Findtheprobability thatthebrakingdistanceis less thanor equalto45m

(c)          Findtheprobability thatthebrakingdistanceis greaterthan

46.8m

(d)         Findtheprobability thatthebrakingdistanceis between45m and46.8m

18. Adrugmanufacturerwantstoestimatethemeanheartratefor patientswith acertainheartcondition.Themanufacturerfinds62peoplewith thecondition.Fromthis sample,themeanheartrateis101beats perminutewith astandarddeviationof8.

(a) Finda99%confidenceintervalforthetruemeanheartrateofall peoplewith this condition.

(b) Interpretthis confidenceintervalandwrite asentencethat explainsit.

19. Determinetheminimumrequiredsamplesize ifyouwanttobe

80%confidentthatthesamplemeaniswithin 2units ofthepopulation meangivensigma= 9.4.Assumethepopulationis normally distributed.

20. Asocialserviceworkerwantstoestimatethetrueproportionof pregnantteenagerswho miss atleastonedayofschool perweekon average.Thesocialworkerwantstobewithin 5%ofthetrue proportionwhenusing a90%confidenceinterval.Apreviousstudy estimatedthepopulationproportionat0.21.

(a) Using this previousstudyasanestimateforp,whatsamplesize should beused?

(b) Ifthepreviousstudywasnotavailable,whatestimateforp should beused?

21. Arestaurantclaims thatits speedofservicetimeis less than15 minutes.Arandomselection of49servicetimeswascollected,and theirmeanwascalculatedtobe14.5minutes.Theirstandard deviation is 2.7minutes.Isthereenoughevidencetosupportthe claim atalpha= .07.Performanappropriatehypothesistest,showing eachimportantstep.(Note:1stStep:WriteHo andHa; 2ndStep: DetermineRejection Region; etc.)