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MAT 167: StatisticsTest I: Chapters 1-3Instructor: Anthony TanbakuchiFall 2007Name:Computer / Seat Number:No books, notes, or friends. You may use the attached equation sheet, R, and acalculator. No other materials. If you choose to use R, copy and paste your workinto a word document labeling the question number it corresponds to. When youare done with the test print out the document. Be sure to save often on a memorystick just in case. Using any other program or having any other documents openon 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 13 questions for a total of 40 points on 12 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 1-3 p. 1 of 121. Given the following data collected from a random sample of individual’s heights in cm:170 185 155 168 162 164 280(a) (3 points) If you were asked to calculate the “average” height for this data, what measureof center (mean, median, mode, midrange) would you use? Give a clear reason why youchoose this measure in terms of the data and what the measure represents.(b) (2 points) Compute the measure of center you recommended above for the data.(c) (2 points) Using the Range Rule of Thumb, estimate the standard deviation for the data.(d) (2 points) Compute the standard deviation for the data.Instructor: Anthony Tanbakuchi Points earned: / 9 pointsMAT 167: Statistics, Test I: Chapters 1-3 p. 2 of 122. A certain type of mouse has a mean weight of 500g and a standard deviation of 30g.(a) (2 points) Construct an interval using the Empirical Rule which you would expect 95% ofthe weights to fall within.(b) (2 points) Find the z-score for a mouse with a weight of 445g.(c) (1 point) Would you consider a mouse with a weight of 445g unusual?3. (2 points) “38% of adults in the United States regularly visit a doctor”. This conclusion wasreached by a college student after she had questioned 520 randomly selected members of hercollege. What is wrong with her survey?Instructor: Anthony Tanbakuchi Points earned: / 7 pointsMAT 167: Statistics, Test I: Chapters 1-3 p. 3 of 124. (2 points) Give an example of sampling error.5. (1 point) If the mean, median, and mode for a data set are all the same, what can you concludeabout the data?6. (2 points) Find10C7.Instructor: Anthony Tanbakuchi Points earned: / 5 pointsMAT 167: Statistics, Test I: Chapters 1-3 p. 4 of 127. The following is a modified box plot of final exam scores for two different sections of a statisticsclass taking the same exam.●section.1 section.250 60 70 80 90 100Final Exam Score(a) (1 point) Which section had the highest score on the exam? Give an approximate valuefor the highest score.(b) (1 point) Which section had the higher median score? Give the approximate median scorefor that section.(c) (1 point) A useful measure of variation is the inter-quartile range which is calculated asIQR = Q3 − Q1. Find the approximate IQR for section 2.(d) (1 point) What percent of data lies within the IQR?8. (2 points) What is the probability of randomly selecting three people all born on the same dayInstructor: Anthony Tanbakuchi Points earned: / 6 pointsMAT 167: Statistics, Test I: Chapters 1-3 p. 5 of 12of the year? (Ignore leap years).9. If a couple has 5 children, what is the probability that:(a) (1 point) They have exactly 2 girls and 3 boys (in that order).(b) (2 points) They have at least one boy.10. (3 points) In a blood testing procedure, blood samples from 5 people are combined into onemixture. The mixture will only test negative if all the individual samples are negative. If theprobability that an individual sample tests positive is 0.20, what is the probability that themixture will test positive?11. (3 points) If a class consists of 12 freshmen and 8 sophomores, find the probability of randomlyselecting three students in the following order: a sophomore then a sophomore then a freshmanwithout replacement.Instructor: Anthony Tanbakuchi Points earned: / 9 pointsMAT 167: Statistics, Test I: Chapters 1-3 p. 6 of 1212. (2 points) A cruise ship has 1000 people on it. Of the 1000 people, 25 are crew members. Findthe probability of randomly selecting 10 people without replacement and none of them are crewmembers.13. 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 relative frequency table.(b) (1 point) What is the probability of randomly selecting someone from the study who is inthe age range 10-29?Instructor: Anthony Tanbakuchi Points earned: / 4 pointsMAT67 Exam 1 TanbakuchiName___________________________________Select the best answer from the choices provided.MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.Determine whether the given value is a statistic or a parameter.1)A health and fitness club surveys 40 randomly selected members and found that the averageweight of those questioned is 157 lb.A)ParameterB)Statistic1)Determine which of the four levels of measurement (nominal, ordinal, interval, ratio) is most appropriate.2)Nationalities of survey respondents.A)RatioB)NominalC)IntervalD)Ordinal2)Identify the number as either continuous or discrete.3)The number of stories in a Manhattan building is 22.A)DiscreteB)Continuous3)Identify which of these types of sampling is used: random, stratified, systematic, cluster, convenience.4)A tax auditor selects every 1000th income tax return that is received.A)ConvenienceB)RandomC)SystematicD)ClusterE)Stratified4)Solve the problem.5)On a test of 40 items, Ariel got 31 correct. What percent were correct?A)129.032258%B)77.5%C)1.29032258%D)0.775%5)1A nurse measured the blood pressure of each person who visited her clinic. Following is a relative-frequencyhistogram for the systolic blood pressure readings for those people aged between 25 and 40. Use the histogram toanswer the question. The blood


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UA MATH 167 - Study Notes

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