MAT 167: StatisticsMidterm ExamInstructor: Anthony TanbakuchiSummer 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. If you choose to use R,write what you typed on the test or copy and paste your work into a worddocument labeling the question number it corresponds to. When you are donewith the test print out the document. Be sure to save often on a memory stick justin case. Using any other program or having any other documents open on thecomputer 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 21 questions for a total of 66 points on 10 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 66 total pointsExam Score:MAT 167: Statistics, Midterm Exam p. 1 of 101. The following is a partial list of statistical methods that we have discussed:1. mean2. median3. mode4. standard deviation5. z-score6. percentile7. coefficient of variation8. scatter plot9. histogram10. pareto chart11. box plot12. normal-quantile plot13. confidence interval for a mean14. confidence interval for a proportionFor each situation below, which method is most applicable? To get full points, give a short(1-3 sentence) description as to why your chosen method is appropriate!• If it’s a graphical method, also describe what you would be looking for.• If it’s a statistic, how susceptible to outliers is it?(a) (2 points) A school board thinks that students might do better in morning math classes.They would like to compare the distribution of student math scores for 4 time categories:early morning classes, mid morning classes, early afternoon classes, and late afternoonclasses.(b) (2 points) A clothing manufacturer wants to determine how much variability there is intoddler waist sizes.(c) (2 points) The Tucson realtors association is publishing their semi-annual newsletter andhas an article discussing current housing prices. They would like to publish a single numberInstructor: Anthony Tanbakuchi Points earned: / 6 pointsMAT 167: Statistics, Midterm Exam p. 2 of 10that is representative of the typical house price in Tucson.(d) (2 points) A political science researcher at the U of A wants to estimate the true percentageof Tucson residents who support Obama from a random survey of 1,000 people.2. (1 point) Make a sketch of a normal distribution that has been positively skewed.3. (1 point) What is the area under a positively skewed normal distribution?4. (1 point) If the mean, median, and mode for a data set are not the same, what can you concludeabout the data’s distribution?Instructor: Anthony Tanbakuchi Points earned: / 5 pointsMAT 167: Statistics, Midterm Exam p. 3 of 105. (2 points) Give an example of sampling error.6. In regards to ¯x and the Central Limit Theorem:(a) (2 points) What are the two conditions under which the CLT applies?(b) (2 points) If the conditions are met, what type of distribution will ¯x have?7. (2 points) Under what conditions can we approximate a binomial distribution as a normaldistribution?8. (2 points) Which distribution (normal, binomial, both, or neither) would be appropriate fordescribing:The sampling distribution of the mean for a random sample from a uniformly distributedpopulation using a sample size of 10.9. (2 points) Give a clear specific example of when you would use a population distribution.10. (2 points) Give an example of when you would use a sampling distribution.Instructor: Anthony Tanbakuchi Points earned: / 14 pointsMAT 167: Statistics, Midterm Exam p. 4 of 1011. Super Fruity Chew candy has a mean weight of 500 g and a standard deviation of 10 g.(a) (2 points) Construct an interval using the Empirical Rule which you would expect 95% ofthe weights to fall within.(b) (2 points) Would you consider a candy with weight of 468 g unusual? (State why.)12. 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) (2 points) Construct a relative frequency table.(b) (1 point) What is the probability of randomly selecting someone from the study who isbetween 20-39 years old?Instructor: Anthony Tanbakuchi Points earned: / 7 pointsMAT 167: Statistics, Midterm Exam p. 5 of 10(c) (2 points) Calculate the approximate mean age of the subjects in the study from the datagiven.13. Results from a randomized experiment to compare crop yields (as measured by dried weightof plants in grams) obtained under a control and two different treatment conditions are shownwith a box plot of the data. The researcher who has developed the two new treatments hopesthat at least one increases crop yield as compared to the control group.●ctrl trt1 trt23.5 4.5 5.5treatmentyield weight(a) (1 point) Did any groups contain an outlier? If so which ones?(b) (1 point) What group had the least variability?(c) (1 point) What was the approximate IQR for the control group (ctrl)?(d) (1 point) Which group had the highest median crop yield? What was the median value?Instructor: Anthony Tanbakuchi Points earned: / 6 pointsMAT 167: Statistics, Midterm Exam p. 6 of 1014. (2 points) You would like to conduct a study to estimate (at the 90% confidence level) themean weight of brown bears with a margin of error of 5 lbs. A preliminary study indicates thatbear weights are normally distributed with a standard deviation of 22 lbs, what sample sizeshould you use for this study?15. (2 points) A random sample of 5 men was conducted to determine the mean resting heart rate.Below is the study data in beats per minute.68.9, 71.9, 61.2, 77.9, 74.2Construct a 99% confidence interval for the true population mean resting heart rate for menusing the above data. (Assume σ is unknown and the population is normally dis-tributed.)16. A bag of M&M’s contains 18 red, 12 blue, 8 green, and 7 brown candies.(a) (2 points) What is the probability of randomly selecting a red or brown M&M?Instructor: Anthony Tanbakuchi Points earned: / 6