MAT 167: StatisticsTest I: Chapters 1-4Instructor: Anthony TanbakuchiSpring 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 10 questions for a total of 46 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 46 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 mass in grams be classified as a nominal, ordinal, interval, or ratio levelof measurement?(b) (1 point) Which of the following measures of variation is most effected by outliers:IQR, standard deviation, range(c) (1 point) What percent of data is greater than Q3?(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 median is greater than the mode for a data set, what can you concludeabout the 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) Give an example of sampling error?(h) (2 points) A box plot is a useful tool that can quickly communicate many traits about aset of data. List 4 useful pieces of information that an observer can easily assess using abox plot.(i) (1 point) You scored in the 78thpercentile on the GRE. If 8,000 people took the GRE,how many people had a score at least as high as your score?Instructor: Anthony Tanbakuchi Points earned: / 10 pointsMAT 167: Statistics, Test I: Chapters 1-4 p. 2 of 72. A survey conducted in our class asked 18 students how many hours they work per week. Usethe R output below to answer the following questions.There are 18 data points stored in the variable x, below is the sorted data:> s o r t ( x )[ 1 ] 0 0 0 0 8 8 10 12 13 20 21 30 30 30 30 30 35 50The basic descriptive statistical analysis is as follows:> summary ( x)Min . 1 s t Qu . Median Mean 3 rd Qu. Max .0 . 0 0 8 . 0 0 16.50 18.17 3 0 . 0 0 50 . 0 0> var ( x )[ 1 ] 21 5. 6 76 5> sd ( x )[ 1 ] 14 .6 8 59 3> h i s t ( x , xla b = ”hours ” , main = ”Student Enrollment Data ”)Student Enrollment DatahoursFrequency0 10 20 30 40 500 1 2 3 4 5 6 7(a) (1 point) Use the range rule of thumb to estimate the standard deviation. Is it close tothe actual standard deviation?(b) (1 point) What is P50equal to?(c) (1 point) What is the IQR (inter quartile range) equal to?Instructor: Anthony Tanbakuchi Points earned: / 3 pointsMAT 167: Statistics, Test I: Chapters 1-4 p. 3 of 7(d) (1 point) What percent of the data falls within the IQR?(e) (1 point) What is the mode for the data?(f) (1 point) What is the percentile for a student who works 8 hours per week?(g) (1 point) What is the z-score for the student who is working 50 hours per week?(h) (1 point) Is 35 hours an unusual (outlier) value based on its z score? (Why)(i) (2 points) If someone asked what the typical number of hours worked per week for thisclass was, why would just reporting the mean be misleading? What would you reportin addition to the mean?(j) (1 point) Is the data positively skewed, negatively skewed, or symmetrical?(k) (1 point) Construct an interval using the Empirical Rule which you would expect 95% ofthe data to fall within.Instructor: Anthony Tanbakuchi Points earned: / 9 pointsMAT 167: Statistics, Test I: Chapters 1-4 p. 4 of 7(l) (1 point) Would the Empirical Rule be accurate when used for this data set? Why?3. (1 point) When plotting frequencies tabulated from categorical data, why would a bar graphbe preferable to a pie chart?4. Use the below box plot to answer the following questions.●FEMALE MALE5 10 15Student credits verses gendercredits(a) (1 point) Which gender has a higher median number of credits?(b) (1 point) What is the approximate median number of credits for the females?(c) (1 point) What is the approximate IQR of credits for the males?(d) (1 point) Which gender has a larger range of credits?(e) (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.Instructor: Anthony Tanbakuchi Points earned: / 7 pointsMAT 167: Statistics, Test I: Chapters 1-4 p. 5 of 7BLACK BLOND BROWNCAR 0 2 11PUBLIC 2 0 0TRUCK 1 0 2(a) (1 point) Find the probability of selecting a person with brown hair.(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 car drivers without replacement.(d) (1 point) If you randomly select 4 people with replacement, what is the probability thatat least one uses public transportation?(e) (1 point) Find the probability of selecting a student who drives a truck or a student withbrown hair.(f) (1 point) Find the probability of selecting a person with blond hair given that they are atruck driver.Instructor: Anthony Tanbakuchi Points earned: / 6 pointsMAT 167: Statistics, Test I: Chapters 1-4 p. 6 of 76. A researcher needs to estimate the mean height of corn in a field containing 10,000 corn plants.The corn plants are planted 100 to a row, and there are 100 rows. The researcher wants to takea sample of 100 corn plant heights.(a) (1 point) Describe a method for sampling this population that would be classified as aconvenience sample.(b) (1 point) Describe a method for sampling this population that would be classified as asimple random sample.7. The weather report for this work week (Monday through Friday) states that the probability ofrain is 5% for each day.(a) (1 point) What is