MAT 167: StatisticsTest I: Chapters 1-4Instructor: Anthony TanbakuchiFall 2008Name:Computer / Seat Number:No books, notes, or friends. Show your work. You may use the attachedequation sheet, R, and a calculator. No other materials. Write your work in theprovided space for each problem (including any R work if appropriate). You maynot use personal computers, only use the classroom computer at your desk. Usingany other program or having any other documents open on the computer willconstitute cheating.You have until the end of class to finish the exam, manage your time wisely.If something is unclear quietly come up and ask me.If the question is legitimate I will inform the whole class.Express all final answers to 3 significant digits. Probabilities should be given as adecimal number unless a percent is requested. Circle final answers, ambiguous ormultiple answers will not be accepted. Show steps where appropriate.The exam consists of 8 questions for a total of 40 points on 7 pages.This Exam is being given under the guidelines of our institution’sCode of Academic Ethics. You are expected to respect those guidelines.Points Earned: out of 40 total pointsExam Score:MAT 167: Statistics, Test I: Chapters 1-4 p. 1 of 71. Provide short succinct written answers to the following conceptual questions.(a) (1 point) Would ethnicity be classified as a nominal, ordinal, interval, or ratio level ofmeasurement?(b) (1 point) Which of the following measures of center is least susceptible to outliers:median, mean, midrange, mode(c) (1 point) What percent of data is greater than Q1?(d) (1 point) If the mean, median, and mode for a data set are all the same, what can youconclude about the data’s distribution?(e) (1 point) If the mean is less than the mode for a data set, what can you conclude aboutthe data’s distribution?(f) (1 point) What does the standard deviation represent conceptually in words? (Be concisebut don’t simply state the equation in words verbatim.)(g) (1 point) To determine the proportion of support in Tucson for Vice Presidential candidatePalin, a researcher randomly samples 10 people (using an ideal simple random sample).From the sample data, 70% expressed their support. The researcher was suspicious of theresult so she repeated the study randomly sampling 10 people 3 more times, the resultantstatistics were 30% 70% and 0% respectively. The researcher thinks some sort of mistakehas occurred causing the numbers to change each time the study is repeated. However,after carefully checking the procedures used, no mistake occurred. What type of errorcould we attribute to the variation between the sample results?(h) (2 points) A histogram is a useful tool that can quickly communicate many traits abouta set of data. List 4 useful pieces of information that an observer can easily assess usinga histogram.Instructor: Anthony Tanbakuchi Points earned: / 9 pointsMAT 167: Statistics, Test I: Chapters 1-4 p. 2 of 7(i) (1 point) Your SAT results state that you scored in the 95thpercentile. What does thismean?(j) (1 point) Why would a SAT percentile be preferred over a raw SAT score for collegeadmissions committees?2. A survey conducted in our class asked 24 students how many credits they were enrolled in thissemester. Use the R output below to answer the following questions.There are 24 data points stored in the variable x, below is the sorted data:> s o r t ( x )[ 1 ] 6 10 10 10 11 11 11 12 12 12 12 12 12 13 13 13 14 15 15 16 16 16 17 19The basic descriptive statistical analysis is as follows:> summary ( x)Min . 1 s t Qu. Median Mean 3 rd Qu. Max.6 . 0 0 11.00 12.00 1 2 . 8 3 15 . 0 0 19 . 0 0> var ( x )[ 1 ] 7. 88 4 05 8> sd ( x )[ 1 ] 2. 80 7 85 6> h i s t ( x , xla b = ” c r e d i t s ” , main = ”Student Enrollment Data ”)Student Enrollment DatacreditsFrequency6 8 10 12 14 16 18 200 2 4 6 8(a) (1 point) Use the range rule of thumb to estimate the standard deviation. Is it close tothe actual standard deviation?Instructor: Anthony Tanbakuchi Points earned: / 3 pointsMAT 167: Statistics, Test I: Chapters 1-4 p. 3 of 7(b) (1 point) What is P25equal to?(c) (1 point) What is the IQR (inter quartile range) equal to?(d) (1 point) What percent of the data falls within the IQR?(e) (1 point) What is the percentile for the student who is taking 14 credits?(f) (1 point) What is the z-score for the student who is taking 10 credits?(g) (1 point) Is 6 credits an unusual (outlier) value based on its z score? (Why)(h) (1 point) Is the data positively skewed, negatively skewed, or symmetrical?(i) (1 point) Construct an interval using the Empirical Rule which you would expect 99.7%of the data to fall within.3. A researcher conducts a study in which 1,000 individuals in Tucson are randomly selectedand asked if they prefer orange juice over grape juice. Eighty percent of the respondentspreferred orange juice. The researcher concludes that “Study data indicates that eighty percentof Americans prefer orange juice over grape juice.”(a) (1 point) What is wrong with this conclusion?Instructor: Anthony Tanbakuchi Points earned: / 9 pointsMAT 167: Statistics, Test I: Chapters 1-4 p. 4 of 7(b) (1 point) Restate an appropriate conclusion that can be reached from the study.4. Use the below box plot to answer the following questions.●●●●●FEMALE MALE5 10 15 20Student forearm length verses genderforearm length (in)(a) (1 point) Which gender has a higher median forearm length?(b) (1 point) What is the approximate median forearm length for the females?(c) (1 point) Which gender has a larger variation in forearm length for the middle 50% ofindividuals?(d) (1 point) How many outliers are there in this data set as indicated by the box plots?5. Using the below table for our class to answer the following questions.BLACK BLOND BROWNFEMALE 2 5 11MALE 3 0 3(a) (1 point) Find the probability of selecting a person with brown hair.Instructor: Anthony Tanbakuchi Points earned: / 6 pointsMAT 167: Statistics, Test I: Chapters 1-4 p. 5 of 7(b) (1 point) Would it be unusual to randomly select a person with brown hair?(c) (1 point) Find the probability of randomly selecting three males without replacement.(d) (1 point) If you randomly select 6 people with replacement, what is the probability thatat least one has brown hair?(e) (1 point) Find the probability of selecting a female student or a student with brown hair.(f) (1 point) Find the probability of selecting a person with brown hair given that they