Test 1 Version A STAT 3090 Spring 2018

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1 Multiple Choice: (Questions 1 20) Answer the following questions on the scantron provided using a #2 pencil. Bubble the response that best answers the question. Each multiple choice correct response is worth 3 points. For your record, also circle your choice on your exam since the scantron will not be returned to you. Only the responses recorded on your scantron will be graded. 1. For a class project, a student randomly surveys 45 high school students. Each student is asked How many hours do you work at a part-time job in a typical week? The results are summarized below. Variable: Number of Hours n: 45 Mean: 8.20 Median: 7.00 StDev: 5.3 Min: 0 Max: 24 Q1: 5 Q3: 11 If a boxplot were produced of this information, what data points would be marked as outliers? A. Any points greater than 17. B. Any points greater than 20. C. Any points greater than 16.3 D. Any points greater than customers of a Starbucks on campus were asked to rate the service as excellent, very good, good, fair, or poor. This variable may be classified as which of the following? A. qualitative, nominal B. qualitative, discrete C. quantitative, nominal D. qualitative, ordinal 3. Nearly two-thirds of current U.S. undergraduates are not confident that college will give them the skills or knowledge to succeed in the job market and the workplace. This was the conclusion that was reached after a survey of 32,000 students at 43 randomly selected fouryear institutions in the United States. Which of the following is true? A. The sample was the 32,000 students who were surveyed. B. The population was all undergraduate U.S. students at four-year institutions. C. Approximately two-thirds is a statistic that was determined by the survey. D. All of these responses are true. 1

2 4. In the survey referenced in the previous question, was the objective of the data collection to make an inference or provide descriptive statistics? A. We are unable to determine the objective of the survey. B. The objective of the survey was to provide descriptive statistics. The goal was the collection and organization of the sample data. C. The objective of the survey was to make an inference. The goal was to make a reasonable estimate about the U.S. undergraduate population. D. The objective of the survey was to make an inference. The goal was the collection and organization of sample data. 5. A data set has a mean that is much lower than the median. Which of the following is most likely true? A. The distribution of values is symmetric. B. The distribution of values is skewed left. C. The distribution of values is skewed right. D. The distribution has a few high outliers. 6. A basketball team has 11 players who each are a different height. The team trades its shortest player for a tall center who is now the tallest person on the team. Which one of the following statements is false? A. The mean height of the team will increase. B. The standard deviation of heights might be different. C. The range of heights might be different. D. The median height will remain the same. 7. n Mean Median Sample Sample The table above shows the sample size, the mean and the median for two samples of measurements. What is the mean for the combined sample of 41 measurements? A B C. 32.1(15)+36.2(26) 41 D

3 8. Researchers conducted a cell phone survey of 176 students a large university. Students were asked whether they planned to purchase a new smart phone within the next 6 months. The survey results in the table below are classified by the student s level in school. Yes No Freshman 5 19 Sophomore Junior Senior Which of the following graphs would provide an appropriate display of the survey results? A. A dot plot B. A stem and leaf plot C. A side-by-side stem and leaf plot D. A bar graph 9. The distribution of weights of a female rowing team is bell-shaped with a mean of 138 pounds and standard deviation 8 pounds. What proportion of female rowers will weigh between 130 pounds and 146 pounds? A B C D Which of the following would be the correct interpretation if your Test 1 score has a z-score of 2.0? A. It means that you missed two questions on Test 1. B. It means that you got twice as many questions correct as the average student. C. It means that your score was two points higher than the mean score. D. It means that your score is two standard deviations above the mean for this exam. 3

4 11. The following box plot shows the distribution of grades for a test in a Biology 1010 class. Approximately what proportion of students scored 60 or lower? A. This cannot be determined because we do not know how many students took the exam. B. 75/100 C. 25/100 D. 60/ A survey conducted by Black Flag asked whether the action of a certain type of roach spray was effective in killing cockroaches. Seventy-nine percent of respondents agreed that the roach spray was effective. The number 79% is a A. statistic. B. sample. C. population. D. parameter. 13. The demand for donuts at the local donut shop is an average of 56 dozen donuts per day with standard deviation 6 dozen donuts. Use Chebyshev s Theorem to find the range in which at least 88.89% of the daily demand will reside. A. 47 to 65 dozen B. 41 to 71 dozen C. 44 to 68 dozen D. 38 to 74 dozen 4

5 14. The following shows the grade distribution for the number of points earned on the STAT 3090 Test 1. Number of Points Frequency Earned What class contains the upper quartile (Q3)? A B C D. We cannot determine this from the given information. 15. The manager of a small appliance store decides to give all of his employees a 20% raise. Which of the following is true? A. Both the mean and median salary will increase by 20%. B. The mean salary will increase by 20% but the median salary will remain the same. C. Both the mean and median salary will remain the same. D. The mean salary will remain the same but the median salary will increase by 20%. 16. Which distribution has the higher standard deviation? A. Distribution A B. Distribution B C. The standard deviations are equal since the means are equal. D. The standard deviations are equal since the distributions are symmetric. 5

6 17 Suppose that event E and event F are mutually exclusive. If P(E) = 0.46 and P(F)=0.2, what is P(E or F)? A B C D If events A and B are independent with P(A) = 0.4 and P(A B) = 0.12, find P(B). A. 0.3 B C D A group of individuals was surveyed to investigate the relationship between gender and the number of friends on social media. The results are shown in the table below. Number of Friends More than 150 Men Women According to the survey, what is the probability that an individual will have between friends if they are male? A. 40/95 B. 40/106 C. 55/106 D. 95/ In a certain school 18% of students are enrolled in a foreign language course, 32% are enrolled in a statistics course and 15% are enrolled in a foreign language course and a statistics course. What percent of students are enrolled in a statistics course or a foreign language course? A. 14% B. 35% C. 64% D. 50% 6

7 Free Response: The Free Response questions will count as 40% of your total grade. Read each question carefully. In order to receive full credit, you must show logical (relevant) justification which supports your final answer. You MUST show your work. Answers with no justification will receive no credit. 1. The Department of Agricultural Sciences at Clemson was interested in determining whether a preservative was effective in reducing discoloration in frozen apples. A sample of 50 ripe apples was chosen and was prepared for freezing by slicing each apple into quarters and removing the core. Each sliced apple was placed into a small plastic bag and the bags of apples were then randomly divided into two groups. The 25 bags in the control group were sealed. The preservative was added to the 25 bags containing apples in the treatment group, then the bags were sealed. All bags were stored at 0 C for a period of 4 months. At the end of this time, after the apples were thawed, a technician rated each apple s discoloration from 1 to 10, with a low score indicating little discoloration. A. Was this an observational study or an experiment? Explain your response. (3 pts) Experiment: There was a treatment of the preservative imposed upon the apples OR this meets the criteria of an experiment because there is randomization, replication and a control Grading: 1 pt States experiment 2 pts States reason B. What was the explanatory variable, response variable? (2 pts) Explanatory: the preservative or no preservative Response: the amount of discoloration of the apples Grading: 1 pt Explanatory variable 1 pt Response variable 7

8 The dot plots below show the distributions of the discoloration rating for the control and treatment groups. C. Use the dot plots to answer the following question. Was the preservative effective in reducing the amount of discoloration in the apples? (4 pts) The preservative appears to have reduced the amount of discoloration in the apples. Student should make some attempt to compare location via median or mean or provide evidence that the discoloration rating for the control group is generally higher. Control: Mean = 6.6, median = 7 Treatment: Mean = 5.16, median = 5 Grading: 1 pt States that the preservative was effective 3 pts Justification, deduct 2 points if the student says that the discoloration of the control group was generally higher (or treatment group was lower) but does not give a specific measure to justify this. D. The standard deviation of the amount of discoloration in the treatment group was Describe the meaning of this value in the context of this situation. (2 pts) The standard deviation of describes the average of the difference in each individual discoloration rating and the mean discoloration rating for apples in the treatment group. Grading: 1 Mentions average or mean, no credit if the term average or mean is used but the definition is pt not close to being correct. 1 Mentions deviations from the mean pt 8

9 2. The weights, in pounds, of the 22 members of the 2012 U. S. Women s Olympic Rowing Team are listed in the table below A. Compute the five-number summary for these weights. Show appropriate work. (3 pts) Min: 106 Q1: 6 th value of 160, Med: ( )/2= Q3: 175 MAX: 185 All units are pounds Deduct 1 if no attempt to indicate location. Deduct 1 for each incorrect value up to full credit deducted Deduct 1 for extraneous values (mean, standard deviation) B. Compute the interquartile range and upper and lower fences for outliers. (3 pts) IQR: = 15 Lower: (15)=137.5 Upper: (15)=197.5 pounds 1 pt Correct IQR 1 pt Correct upper fence with work shown 1 pt Correct lower fence with work shown C. Are there outliers in this distribution? If so, justify below. (2 pts) 106, 123, and 130 pounds are outliers because they are lower than the lower fence. **Deduct 1 point if the unit (pounds) is not indicated anywhere in part A, part B or part C 1 pt Correctly identifies the 3 outliers no deduction for unit 1 pt Compares to lower fence D. Sketch the boxplot of the distribution of weights on the grid below. (3 pts) Weights (pounds) 1 pt Box and right whisker drawn correctly 1 pt Left whisker drawn correctly 1 pt Outliers correct No partial credit for any part 9

10 3. A sample of 81 teenagers was asked how many movies they watched from beginning to end during the past month. Students reported integer values (0, 1, 2, ). The graph below summarizes the results Frequency Number of Movies 5 6 A. Use the graph to compute the mean number movies seen in the last month by this group of teenagers. Justify your answer. (4 pts) x = 0(26) + 1(24) + 2(14) + 3(8) + 4(6) + 5(2) + 6(1) pt Correct symbol for mean or word mean, correct unit 1 pt Correct numerator 1 pt Correct denominator 1 pt Correct answer = 1.43 movies B. From this data, it was determined that the standard deviation of the number of the number of movies seen is 1.45 movies. Use the mean that you found in part A, to compute the interval from one standard deviation below the mean to one standard deviation above the mean. (2 pts) = = 2.88 The range is from 0 to 2.88 movies 1 pt Correct upper limit with work shown 1 pt Correct lower limit with work shown 10

11 C. Find the percent of data represented by the graph that falls inside the interval from one standard deviation below the mean to one standard deviation above the mean. Justify. (2 pts) From the graph: ( )/ 81 ~ 79% No partial credit. If an incorrect range from part B is used in a correct manner, give credit. D. Is the percent of data falling within one standard deviation of the mean close to what the Empirical Rule predicts? What is the reason for this discrepancy? (3 pts) The Empirical Rule predicts that approximately 68% of the data in a bell-shaped distribution lies within one standard deviation of the mean. This distribution is not bell-shaped so the Empirical Rule does not apply. 1 pt Correct reference to Empirical Rule 2 pts Explanation of discrepancy based upon the shape of the distribution. 11

12 4. The Carolina Farm Cooperative owns and leases prime farmland in the Southeast. Most of its acres are planted in corn. The cooperative performs a substantial amount of testing to determine what seed types produce the greatest yields. Recently the cooperative tested three types of corn seed on test plots. The following values were observed after the first year: Mean (bushels per acre) Standard Deviation (bushels per acre) Seed Type A Seed Type B Seed Type C A. Based on the results of the testing, which seed produced the greatest yield per acre? Justify. (2 pts) Seed type C has the highest mean yield. 1 pt Chooses seed type C 1 pt States highest mean yield. B. Assume that the production of each type of seed is bell-shaped and the Empirical Rule applies to each distribution. If you are a farmer and had to obtain at least 135 bushels per acre to escape bankruptcy, which seed type would you plant? Explain your choice clearly. (4 pts) Seed Type A: Student should compare the relative position of 135 acres in all three distributions: z-score for A = 1.88 z-score for B = 5.27 z-score for C = 2.19 There is a higher likelihood of a yield of 135 acres or more for Seed Type A because the z- score associated with 135 acres is the lowest in distribution A. 1 pt Chooses seed type A 3 pts Correct justification based upon relative position. 12

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14 NAME: SECTION: Did you bubble your CID and test form correctly? 14

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