EXS_EX.3.2007Fall

# EXS_EX.3.2007Fall - SOLUTIONS MAT 167 Statistics Final Exam...

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SOLUTIONS MAT 167: Statistics Final Exam Instructor: Anthony Tanbakuchi Fall 2007 Name: Computer / Seat Number: Multiple choice part: ﬁll in answer on the scan form. Do not attach work for this section (no partial credit is awarded). Written part: Write all ﬁnal answers on the exam. Actual work should be attached so partial credit can be given. No books, notes, or friends. You may use the attached equation sheet, R, and a calculator. No other materials. If you choose to use R, copy and paste your work into a word document labeling the question number it corresponds to. When you are done with the test print out the document. Be sure to save often on a memory stick just in case. Using any other program or 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 a decimal number unless a percent is requested. Circle ﬁnal answers, ambiguous or multiple answers will not be accepted. Show steps where appropriate. The exam consists of 9 questions for a total of 36 points on 15 pages. This Exam is being given under the guidelines of our institution’s Code of Academic Ethics . You are expected to respect those guidelines. Points Earned: out of 36 total points Exam Score:

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MAT 167: Statistics, Final Exam SOLUTIONS p. 1 of 15 1. Given the following data from a random sample: 21 11 21 14 20 26 17 220 (a) (1 point) Find the mean of the data. Solution: > mean(x) [ 1 ] 43.75 (b) (1 point) Find the median of the data. Solution: > median (x) [ 1 ] 20.5 (c) (1 point) Since the mean and the median are not equal, what does this indicate about the data? Solution: The data is skewed. (d) (1 point) Which measure of center (mean or median) do you think is better for describing this data and why ? Solution: (Answers may vary somewhat) This data set contains one outlier so the median would be a better measure of the center since it is less susceptible to outliers. (e) (1 point) Find the standard deviation of the data. Solution: > sd (x) [ 1 ] 71.36576 2. In regards to ¯ x and the Central Limit Theorem: (a) (1 point) What are the two conditions under which the CLT applies? Solution: Either (1) x has a normal distribution or (2) n > 30. (b) (1 point) If the conditions are met, what does the CLT state about ¯ x ? Solution: The sampling distribution of ¯ x will have a normal distribution. 3. The following are histograms of student scores on the same exam for two diﬀerent sections of a statistics class. Instructor: Anthony Tanbakuchi Points earned: / 7 points
MAT 167: Statistics, Final Exam SOLUTIONS p. 2 of 15 Section 1 score Frequency 0 20 40 60 80 100 0 5 10 15 Section 2 score 0 20 40 60 80 100 20 (a) (1 point) Which section had a higher mean score?

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EXS_EX.3.2007Fall - SOLUTIONS MAT 167 Statistics Final Exam...

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