Math 155, Test 1, 18 October 2011 Name: Instructions. This is a closed-book test. You may use a calculator (but not a cell phone). Make sure all cell-phones are put away and that the ringer is off. Show work on questions where appropriate, and write final answers in spaces provided. 1. (3 pts) To compute the average amount of medical insurance its patients had in 2010, a hospital considered taking the following types of samples. For each case classify the sample as simple random, stratified, systematic, cluster, convenience. (a) The hospital randomly chose a patient in 2010, and collected data from that patient and every 200th patient admitted thereafter in 2010. (b) The hospital numbered its complete list of patients from 2010 and used a random number generator to select 100 patients from the list from which to collect the data. (c) The hospital decided to collect the data from the first 50 patients admitted on July 4, 2010. 2. (4 pts) Categorize the following data according to level: nominal, ordinal, interval, or ratio. (a) The name of the city in which a marathon is run. (b) Difficulty level of a marathon: low, medium, high. (c) The length of time it takes for someone to run a marathon. (d) The time of day a marathon starts. 3. (4 pts) (a) Given a collection of ordered data with 85 numbers, in what position is the median? (b) What percentile is the first quartile Q 1? (c) In a set of data, approximately what percentage of the data lie at or above the 53rd percentile? (d) If you are among 2000 students taking the MCAT, and you wish to score at least the 92nd percentile, what is the maximum number of students that can score at least as well or better than you?
4. Consider the following set of 29 numbers. 1 2 3 4 6 14 18 22 26 30 35 36 37 38 42 44 45 48 52 52 53 54 56 58 60 62 68 70 77 Note: x = 1113 and x 2 = 56539 (a) (1 pt) Find the mean (b) (1 pt) Find Q 1 (c) (2 pts) Find the sample variance (d) (1 pt) Find the sample standard deviation (e) (3 pts) Complete the following row of a frequency table for the data given a class width of 10. Lower Upper Lower Upper Relative Cumulative Limit Limit Boundary Boundary Frequency Frequency Frequency 40 5. (2 pts) Consider two populations where the first has a mean of 100 and the second has a mean of 25. Which of the following must be true? (a) The first population has a larger median than the second. (b) The first population has a larger standard deviation than the second. (c) The second population has a larger median than the first. (d) The second population has a larger standard deviation than the first. (e) None of the above.
6. (6pts) With reference to the histogram below based on a data set of size 50, answer the following questions: (a) Find the frequency of the class with lower boundary 155.5: (b) Find the relative frequency of the class with lower boundary 155.5: (c) What is the class width? (d) What is the upper limit of the fourth class? (e) What is the class mark of the fourth class? (f) Which choice below best describes the shape of the distribution? (A) symmetrical (B) bimodal (C) skewed to the right (D) skewed to the left (E) none of the above 7. (4 pts) (a) Given a set of data that ranges from 10 to 82. Use the book s formula to compute the class width needed to create a frequency table with 6 classes? (b) With the class width as in (a), what would the limits of the second class be? Lower limit: Upper limit:
8. (4 pts) Use the ogive below to answer the following questions. (a) What is the frequency of the second class? (b) What is the cumulative frequency of the second class? (c) What is the relative frequency of the second class? (d) How many winning times fell between 2:03.15 and 2:11.15? 9. A population is known to have a mean of 60 and a standard deviation of 7. (a) (2 pts) Use Chebyshev s theorem to find an interval that contains at least 8 9 of the data. (b) (2 pts) According to Chebyshev s theorem at least what portion of data is contained in the interval from 32 to 88? 10. (2 pts) Consider two populations where the first has a standard deviation of 100 and the second has a standard deviation of 25. Which of the following is correct? (a) The first population has a smaller mean than the second. (b) The first population has a smaller variance than the second. (c) The second population has a smaller variance than the first. (d) The second population has a smaller mean than the first. (e) None of the above.
11. (4 pts) Consider the two populations each having 18 elements whose stem and leaf plots are given below. Population 1 Population 2 10 9 14 1 = 141 11 1 6 6 8 8 8 9 12 0 2 2 3 3 5 6 13 4 4 14 1 (a) Which population has the smaller mean (do not compute them)? 4 1 2 7 8 4 7 = 47 5 2 7 6 1 2 5 7 0 8 4 4 4 9 0 1 2 2 10 5 (b) Which population appears to have the smaller variance (do not compute them)? (c) Find the range of Population 2: (d) Find the median of Population 1: 12. (3 pts) An airline files out of Seattle, Los Angeles and Denver. From these cities, 90 percent of its 500 flights from Los Angeles were on-time; 70 percent of its 150 flights out of Seattle were on-time; and 80 percent of its 350 flights out of Denver were on-time. Use a weighted average to compute its overall on-time percentage. Express answer to nearest tenth of a percent. 13. (3 pts) A large set of data includes numbers from 13 to 51 has Q 1 = 20, Q 3 = 40 and a median of 35. Sketch a box-and-whisker plot for the data.