{2 points}Name ______

You MUST workalone– no tutors; no help from classmates. Emailmeorsee mewith questions. You will receive a scoreof0 ifthis ruleis violated. Classroom Lab is open on Monday from 9am-3pm.

EPE/EDP660 EXAM1: Summer2015

{3points}Minitab(orotherapprovedsoftware)outputmustbeincluded.Itmustbeclearly labeled,with allanswersclearlyidentified.You may also choose to copy output and embed within the exam responses.Youmust alsoincludeacopyofyoursessionwindow. Make sure to enable commands in the worksheet.DoNOT includea copyof theworksheet.

Directions:Read each question beforeresponding.In order to receive partial credit, work must be shown.

PART A (33POINTS):FILL IN THE BLANK(with best choice) {1 point perblank}

  1. The field of statistics can be roughly divided into two areas (also known as branch of statistics): ______and ______.
  2. The mean, , and standard deviation, , completely specify the ______distribution.
  1. If we think that a variable, x, may explain or even cause changes in another variable, y, we call x a(n) ______variable and y a(n) ______variable.
  2. The ______measures the direction and the strength of the linear association between two variables.
  1. Fill in the following table with OK, Type I error, or Type II error.

Null Hypothesis

Decision / Ho True / Ho False
Fail to Reject Ho /
Reject Ho /
  1. At a UK basketball game, 500 fans were randomly selected and asked how much they paid for parking. From this group amean of $14 wascomputed. Match theitems in ColumnIIwith thestatistical term in ColumnI.

ColumnI / ColumnII
___Statistic
___ Data
___Sample
___Population / (a)500 selected fans
(b)All fans in attendance
(c)The amount paid for parking by each of the
500 selected fans
(d) The computed $14

Use the following Table to answer # 7 – 12.

ID / Anxiety [0-100%] / Sex / Result on Test
1 / 25 / F / Fail
2 / 2 / F / Pass
3 / 77 / F / Pass
4 / 56 / M / Pass
5 / 95 / M / Fail
6 / 0 / M / Pass
  1. What type of variable is ID?____

A.Nominal

B.Ordinal

C.Interval

D.Ratio

  1. What type of variable is Sex? ____

A.Nominal

B.Ordinal

C.Interval

D.Ratio

  1. What type of variable is Anxiety? ____

A.Nominal

B.Ordinal

C.Interval

D.Ratio

  1. What type of variable is Result on Test? ____

A.Nominal

B.Ordinal

C.Interval

D.Ratio

  1. What type of variable is ID? ____

A.Categorical

B.Numerical

  1. What type of variable is Anxiety? ____

A.Categorical

B.Numerical

Use the following equation to answer

E(y) = β0 + β1x

  1. β0 and β1 are ______.

A.Population parameters

B.Sample statistics

C.Intercepts

D.Slope estimates

  1. What is the y-intercept when x is 0?____

A.E(y)

B.β0

C.β1

D.x

  1. What is the slope estimate?____

A.E(y)

B.β0

C.β1

D.x

Fill in the blank with either “A” for True or “B” for False.

  1. The mean is a measure of central tendency. ____

A.True

B.False

  1. If a density curve is perfectly symmetric, the mean, median, and mode are the same. ____

A.True

B.False

  1. The ε is a random variable with mean = 1 and variance σ2. ____

A.True

B.False

  1. R-square (R2) values range between 0 and 100%. ____
  1. True
  2. False
  1. Pearson correlation values range between 0 and 1. ____

A.True

B.False

  1. To test if the slope parameter is zero, we use at –test. ____
  1. True
  2. False
  1. SST does not change with the model, as it depends only on values of the dependent variable, y. ____
  1. True
  2. False
  1. SSE decreases as variables are added to a model, and SSM increases by the same amount. ____
  1. True
  2. False
  1. In a hypothesis test, if the p-value = 0.08 and you have set alpha at 0.05, the decision would be to Reject the null hypothesis. ____

A.True

B.False

  1. Sum of Squares measure the amounts of explained and unexplained information due to the model ____.

A.True

B.False

PART B(18 POINTS): SHORT ANSWER

Answer thefollowingquestions inafewsentences.

  1. Central tendency can be measured by the mean, median, and mode. Briefly describe each one providing an example of when it might be used. {3 points}
  1. What three components do you need to produce a confidence interval? Why do statisticians prefer confidence intervals over point estimates? {3 points}
  1. A researcher demonstrates that the number of statistics courses taken ishighly negatively correlated with exam anxiety. She goes on to argue that increases the numbers of statistics’ classes students take will cause a decrease in exam anxiety. Is this a reasonable argument? Explain. {4 points}
  1. Asagraduatestudentdiscussestheresultsofastudyheconducted,aclassmatesuggestshehas committed a TypeII error. Whatdoesthismean,andwhatmightthestudentdotoguardagainst makingthis typeof errorin the future?Be specific about how the adjustment would help. {4 points}
  1. A teacher fits a regression model using age to predict effort. For the model, Minitab reports a R-square value of 0.63. The teacher argues that while this may not be the best estimate, it is good. Do you agree? Explain. {4 points}

PART C (44POINTS):DATA ANALYSIS

1. Aresearcherwantstoinvestigatetherelationshipbetweenstudents’“self-concept”andtheir academic performance.The researcher isspecifically interestedinhowmuch“self-concept”contributestoexplaining GPA aftertheeffectofIQistakenintoaccount.Thestudyincludesasampleof78seventh-gradestudents inaruralMidwesternschool.Thevariablesincludeeachstudent’sgradepointaverage(GPA),score on astandardIQ test (IQ), and scoreon the Piers-Harris Children’s Self-Concept Scale (Self-concept).

A. Producedescriptive statistics(be sure toproduce ata minimumthemean,median,nandstandard deviation) ofGPA,IQ,and Self-Concept(you maywish to usegraphical summary). {3 points}

B. Discussthedistributionofeachvariable,intermsofcentraltendencyandvariation.Youmay also wish to discuss thegeneral shapeof theplotted variables.{3 points}

C. NowinvestigatethepotentialeffectofIQonGPA:CreateascatterplotofGPAversusIQ.

{1point};Calculatethecorrelationestimatebetweenthesetwovariables.{1point};Performa simple linear regression.{2 points}You are not required to check assumptions here.

D. Nowinvestigatethepotentialeffectofstudent’sself-conceptontheGPA:Createascatterplotof GPA versus self-concept {1 point}; Calculate the correlation estimate between these two variables. {1 point}; Perform a simple linear regression. {2 points}You are not required to check assumptions here.

E. Which variable appears to havethegreatest variation?Explain.{2 points}

F. Doyoufeel thatbothIQand Self-concept areuseful predictors of GPA?Explain.{3 points}

2. Aresearcherisinterestedinestimatingbirthratesforyoungmothers(ages15-17)fromthepoverty rateinthestateinwhichthey live.HeconsultstheU.S.CensusBureaufortheyear2000.Herecords thestatename (Location),percentageofpopulationliving inhouseholdswithincomebelowpoverty level(PovPct)andbirthratefor females15to17yearsold(Brth15to17).Birthratereferstobirthsper1,000 persons in thegroup.

A. Create ascatterplot of PovPct (x) and Brth15to17 (y).{1point}

B. Basedonyourplot,describethestrengthanddirectionoftherelationshipbetweenBirthRate (y)and Percent of Poverty(x).{2 points}

C. Doyoufeelthatsimplelinearregressionisa sound choicein this setting?Explain. You are not being asked to run the regression at this point. {2points}

D. Computetheleast-squaresregressionequation,R-square, andcoefficientestimates.Besuretoalso createthe 4-1 plotto check the assumptions of regression.{3points}

E. Aretheassumptionssatisfiedforlinearregression?Discussintermsoftheplots.Providedetailof either support or non-support. {3 points}

F. Write the most accurate least-squares regression equation using your output. {1 point}

G. Interpretyour slope(b1) in the context of thesevariables.{2points}

H. Test ifb0 andb1 aresignificant. Is one of these tests more important? Why? {3points}

  1. Report andInterpretyourR-squarevalue. {2points}
  1. Identifyand report anyextreme values inyour data set.If none, state that.{2 points}

K. GivenaPovPctof68,useyourregressionequationtopredicttheexpectedbirthrate.(Showyou work). Doyou have anyissues with this estimate?Explain.{2points}

L. Produce the line of best fit, be sure to include 95% Confidence and Prediction intervals on your graph. {2 points}