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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. Using any other programor having any other documents open on the computer will constitute 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 35 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 35 total pointsExam Score:MAT 167: Statistics, Test I: Chapters 1-4 p. 1 of 71. Provide short written answers to the following conceptual questions.(a) (1 point) Is the range rule very susceptible to outliers?(b) (1 point) What percent of data lies within the IQR?(c) (1 point) What does the z-score represent in words?(d) (1 point) What does the standard deviation represent in words?(e) (1 point) A student needs to quantitatively describe the variation of the heights of studentsin a class. In comparison to variance, what important characteristic of standard deviationmakes it more useful for communicating the amount of variation in the heights?(f) (2 points) Give an example of sampling error.(g) (1 point) If the mean, median, and mode for a data set are different, what can you concludeabout the data’s distribution?Instructor: Anthony Tanbakuchi Points earned: / 8 pointsMAT 167: Statistics, Test I: Chapters 1-4 p. 2 of 72. A survey conducted in our class asked 27 students how far they travelled to school (in miles).Use the R output below to answer the following questions.There are 27 data points stored in the variable x, below is the sorted data:> s o r t ( x )[ 1 ] 0 .1 0 . 1 3 . 5 4 . 0 4 . 5 5 . 0 5 . 0 5 . 0 5 . 0 6 . 0 6 . 0 7 . 3 8 . 09 . 0 1 0 . 0[ 1 6 ] 11 . 8 12 . 0 1 2 . 5 1 3 .0 13 . 0 13. 0 1 5 .0 16 . 0 20. 0 2 0 .0 2 7 . 0 40 . 0The basic descriptive statistical analysis is as follows:> summary ( x )Min . 1 s t Qu . Median Mean 3 rd Qu . Max.0 . 1 0 5 . 0 0 9 . 0 0 10 . 8 1 1 3.00 4 0 . 0 0> var ( x )[ 1 ] 7 3 . 9 1148> sd ( x )[ 1 ] 8 . 5 9 7179> h i s t (x , xla b = ”commute d i s t a n c e s ( m i l e s ) ” , main = ”Student commuting data ”)Student commuting datacommute distances (miles)Frequency0 10 20 30 400 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?(b) (1 point) What is P25equal 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) For the student who commutes 4.5 miles to school, what is their approximatepercentile?(e) (1 point) What is the z-score for the student who commutes 40 miles to school?(f) (1 point) Is 40 miles an unusual (outlier) distance based on it’s z score?(g) (1 point) Which measure of center would you use to describe this data? 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 68% ofthe data to fall within.(j) (1 point) Would the Empirical Rule be appropriate to use for this data set? Why?Instructor: Anthony Tanbakuchi Points earned: / 7 pointsMAT 167: Statistics, Test I: Chapters 1-4 p. 4 of 73. “The average commute distance of US community college students is 10.8 miles.” This conclu-sion was reached by a student who had surveyed his statistics class.(a) (1 point) What type of sampling did the study use?(b) (1 point) Briefly state what is wrong with the student’s conclusions.4. Use the below box plot to answer the following questions.FEMALE MALE0 10 20 30 40 50Student work hours verses genderwork hours / week(a) (1 point) Which gender has a higher median number of work hours?(b) (1 point) What is the approximate median work hours / week for the females?(c) (1 point) Which gender has a larger variation in work hours for the middle 50% of indi-viduals?(d) (1 point) What is the maximum hours per week observed for the male data?Instructor: Anthony Tanbakuchi Points earned: / 6 pointsMAT 167: Statistics, Test I: Chapters 1-4 p. 5 of 75. Using the below table for our class to answer the following questions.BLACK BLOND BROWN REDFEMALE 1 5 12 2MALE 1 0 5 1(a) (1 point) Find the probability of selecting a person with red hair.(b) (1 point) Would it be unusual to randomly select a person with red hair?(c) (1 point) Find the probability of randomly selecting three males without replacement.(d) (1 point) If you randomly select 5 people with replacement, what is the probability thatat least one has red hair?(e) (1 point) Find the probability of selecting a male student or a student with red hair.Instructor: Anthony Tanbakuchi Points earned: / 5 pointsMAT 167: Statistics, Test I: Chapters 1-4 p. 6 of 7(f) (1 point) Find the probability of selecting a person with red hair given that they are male.6. (1 point) With one method of a procedure called acceptance sampling, a sample of items israndomly selected without replacement and the entire batch is accepted if every item in thesample is okay. The Niko Electronics Company has just manufactured 10,000 CDs, and 500are defective. If 5 of the CDs are randomly selected for testing without replacement, what isthe probability that the entire batch will be accepted?Instructor: Anthony Tanbakuchi Points earned: / 2 pointsMAT 167: Statistics, Test I: Chapters 1-4 p. 7 of 77. Given the following frequency table summarizing data from a study:age.years frequency0-9 5.0010-19 8.0020-29 12.0030-39 2.00(a) (1 point) Construct a cumulative frequency table.(b) (1 point) What is the probability of randomly selecting someone from the study who 19years or younger?8. (2 points) Given x = {4c, 2c, −2c}, where c is a constant, completely simplify the followingexpression:rP(xi− 2c)25Instructor: Anthony Tanbakuchi Points earned: / 4 pointsBasic Statistics: QuickReference & R Commandsby Anthony Tanbakuchi. Version


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