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STAT 202, SAFI Thursday, Sep. 25th, 03 NAME: __________________________________ ID:________________ CODE:________ SECTION 1: MULTIPLE-CHOICE For each question in this section, circle the correct answer. (Problem is worth 4 pts.) Questions 1-2 refer to the following information: The average hourly wage at a fast food restaurant is $5.85 with a standard deviation of $0.35. Assume that the wages are normally distributed. 1. The minimum and the maximum wages of the middle 95% of workers are: (a) 5.50 and 6.20 (b) 5.15 and 6.55 (c) 4.80 and 6.90 (d) 5.25 and 6.45 2. The probability that a selected worker earns more than $6.90 is (a) 0.9987 (b) 0.4987 (c) 0.0013 (d) Essentially 0. 3. In order to be accepted into a top university, applicants must score within the top 5% on the SAT exam. Given that the test has a mean of 1000 and a standard deviation of 200, what is the lowest possible score a student needs to qualify for acceptance into the University? (a) 1330 (b) 1400 (c) 1250 (e) 1100 4. The weekly earnings of bus drivers are normally distributed with a mean of $395. If only 1.1% of the bus drivers have a weekly income of more than $429.35, the standard deviation of the weekly earnings of the bus drivers is (a) 2.29 (b) 34.35 (c) 31.23 (d) 15 5. Which of the variables below is categorical? (a) County of residence (b) Number of people, both adults and children, living in the household (c) Total household income, before taxes (d) Age of respondent 1 6. Which of the following is true about the correlation coefficient r? (a) It is a resistant measure of association. (b) -1≤ r ≤1 (c) If r is the correlation coefficient between X and Y, then -r is the correlation coefficient between Y and X. (d) All of the above. 7. The sum of deviations of the individual data elements from their mean is a. always greater than zero b. always less than zero c. sometimes greater than and sometimes less than zero, depending on the data elements d. always equal to zero 8. During a cold winter, the temperature stayed below zero for ten days (ranging from -20 to -5). The variance of the temperatures of the ten day period a. is negative since all the numbers are negative b. must be at least zero c. cannot be computed since all the numbers are negative d. can be either negative or positive 9. Social security numbers consist of numeric values. Therefore, social security is an example of a. a quantitative variable b. either a quantitative or a qualitative variable c. an exchange variable d. a qualitative variable 10. If a data set has an even number of observations, the median a. cannot be determined b. is the average value of the two middle items c. must be equal to the mean d. is the average value of the two middle items when all items are arranged in ascending order Questions 11-12 refer to the following information: A researcher has collected the following sample data: 3 11. The standard deviation is a. 8.944 b. 4.062 c. 13.2 d. 16.5 12. The interquartile range is a. 11 b. 5.5 c. 6 d. 12 2 5 12 3 2 13. A financial analyst's sample of six companies' book value were $25 $7 $22 $33 $18 $15 The sample mean and sample standard deviation are (approximately): (a) (b) (c) (d) 20 and 79.2 respectively 20 and 8.9 respectively. 20 and 8.12 respectively. 120 and 8.9 respectively. Questions 14 through 15 refer to the following information: Here is a stem-plot of the percent of adult males who are illiterate in 142 countries (only 88 included in this study), according to the United Nations for year 1995. For example, the highest illiteracy rate was 72%, in the African country Burkina Faso. 0 0 1 1 2 2 3 3 4 4 5 5 6 6 7 00000000001111112233344 55677788 0000001122234 55689 02344 567 004 6667788899 13 58 0233 6 14 788 2 14. The mean of this distribution (don't try to find it) is certainly (a) Very close to the median. (b) Clearly less than the median. (c) Clearly greater than the median. (d) Can’t say because the mean is random. 15. Based on the shape of this distribution, what numerical measures would best describe it? (a) The five-number summary. (b) The mean and standard deviation. (c) The mean and the quartiles. (d) The mean and the correlation coefficient. 3 SECTION 2: FREE-RESPONSE PROBLEMS Question #1 (5 Points) A data has a first quartile of 42 and a third quartile of 50. Compute the lower and upper limits. Should a data value of 65 be considered an outlier? Question #2 1. [15 points] Sarah’s parents are concerned that she seemed short for her age. Their doctor has the following record of Sarah’s height: Age (months) Height (cm) 36 86 48 90 51 91 54 93 57 94 60 96 (a) (3 Points) Find the correlation coefficient between the two variables. (b) (3 Points) Find the equation of the least-squares regression line of height on age. (c) (3 Points) Predict (d) (3 Points) Provide Sarah’s height at 40 months. an interpretation for the slope of the regression line. (e) (3 Points) Find r 2 and provide an interpretation about it. 4 Question #3: [20 points] The sales record of a real estate company for the month of May shows the following house prices (rounded to the nearest $1,000). Values are in thousands of dollars. 140 (a) (5 Points) Find (b) (4 points) 55 45 85 75 50 60 75 80 95 the five-number summary for the house prices. Five-number summary Find the mean. Explain why the mean and median are different for this particular set of data. (c) (8 Points) Construct 40 (d) (3 Points) 50 60 a labeled boxplot for the house prices. (Show all your work). 70 80 90 100 110 120 Describe the distribution of the house prices. 5 130 140 150