Benchmark Assessment PDF

Benchmark assessment: Based off of Priority Standards determined by the faculty using the South Carolina College and Career Readiness Mathematical Standards PS.SPMJ.1* Understand statistics and sampling distributions as a process for making inferences about population parameters based on a random sa...

Benchmark assessment: Based off of Priority Standards determined by the faculty using the South Carolina College and Career Readiness Mathematical Standards PS.SPMJ.1* Understand statistics and sampling distributions as a process for making inferences about population parameters based on a random sample from that population. PS.SPMJ.3 Plan and conduct a survey to answer a statistical question. Recognize how the plan addresses sampling technique, randomization, measurement of experimental error and methods to reduce bias. PS.SPID.1* Select and create an appropriate display, including dot plots, histograms, and box plots, for data that includes only real numbers. PS.SPID.2* Use statistics appropriate to the shape of the data distribution to compare center and spread of two or more different data sets that include all real numbers. PS.SPID.3* Summarize and represent data from a single data set. Interpret differences in shape, center, and spread in the context of the data set, accounting for possible effects of extreme data points (outliers) PS.SPID.7* Find linear models using median fit and regression methods to make predictions. Interpret the slope and intercept of a linear model in the context of the data PS.SPCR.2 Use the multiplication rule to calculate probabilities for independent and dependent events. Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent. 1. Parking at a large university has become a very big problem. University administrators are interested in determining the average parking time (e.g. the time it takes a student to find a parking spot) of its students. An administrator inconspicuously followed 120 students and carefully recorded their parking times. Identify the population of interest to the university administration. A) the parking times of the entire set of students that park at the university B) the parking times of the 120 students from whom the data were collected C) the entire set of faculty, staff, and students that park at the university D) the students that park at the university between 9 and 10 AM on Wednesdays 2. Parking at a large university has become a very big problem. University administrators are interested in determining the average parking time (e.g. the time it takes a student to find a parking spot) of its students. An administrator inconspicuously followed 180 students and carefully recorded their parking times. Identify the sample of interest to the university administration. A) location of the parking spot B) parking time of a student C) parking times of the 180 students D) type of car (import or domestic) 3. the number of calls received at a companyʹ s help desk A) qualitative B) quantitative 4. the native languages of students in an English class A) qualitative B). quantitative 5. the weight of a player on the wrestling team A) continuous B) discrete 6. the number of goals scored in a hockey game A) continuous B) discrete 7. height of a tree A) nominal B) ratio C) ordinal D) interval 8. the native language of a tourist A) nominal B) ratio C) ordinal D) interval 9. the day of the month A) nominal B) ratio C) ordinal D) interval 10. A scientist was studying the effects of a new fertilizer on crop yield. She randomly assigned half of the plots on a farm to group one and the remaining plots to group two. On the plots in group one, the new fertilizer was used for a year. On the plots in group two, the old fertilizer was used. At the end of the year the average crop yield for the plots in group one was compared with the average crop yield for the plots in group two. A) experiment B) observational study 11. A researcher obtained a random sample of 100 smokers and a random sample of 100 nonsmokers. After interviewing all 200 participants in the study, the researcher compared the rate of depression among the smokers with the rate of depression among nonsmokers. A) experiment B) observational study 12. The names of 30 employees are written on 30 cards. The cards are placed in a bag, and three names are picked from the bag. What sampling technique was used? A) simple random B) stratified C) cluster D) convenience E) systematic 13. An education researcher randomly selects 60 of the nation’s junior colleges and interviews all of the professors at each school. What sampling technique was used? A) simple random B) stratified C) cluster D) convenience E) systematic 14. The Excel frequency bar graph below describes the employment status of a random sample of U.S. adults. What is the percentage of those having no job? A) cannot be determined B) 15% C) 20% D) 40% 15. Determine the number of classes in the frequency table below. Class Frequency 38- 39 7 40- 41 2 42- 43 6 44- 45 4 46- 47 1 A) 1 B) 2 C) 5 D) 20 16. For the stem- and- leaf plot below, what are the maximum and minimum entries? 1| 05 1 |. 6 6 6 7 8 9 2 |. 0 1 1 2 3 4 4 5 6 6 2 |. 7 7 7 8 8 9 9 9 3 |. 0 1 1 2 3 4 4 5 5 3|. 6 6 6 7 8 8 9 9 4 |. 0 9 A) max: 40; min: 10 B) max: 38; min: 7 C) max: 47; min: 15 D) max: 49; min: 10 17. Describe the shape of the distribution. A) skewed to the left B) skewed to the right C) uniform D) bell shaped 18. The data set: ages of dishwashers (in years) in 20 randomly selected households 12 6 4 9 11 1 7 8 9 8 9 13 5 15 7 6 8 8 2 1 A) uniform B) bell shaped C) skewed to the left D) skewed to the right 19. Is either histogram symmetric? A) Neither is symmetric. B) The first is symmetric, but the second is not symmetric. C) The second is symmetric, but the first is not symmetric. D) Both are symmetric. 20. The grade point averages for 40 evening students are listed below. Grade Point Average Frequency 0.5- 0.9 4 1.0- 1.4 2 1.5- 1.9 7 2.0- 2.4 9 2.5- 2.9 2 3.0- 3.4 10 3.5- 3.9 2 4.0- 4.4 4 What is the percentage of students with a 3.5-3. GPA? A) 25% B) 50% C) 5% D) 10% 21. Listed below are the ACT scores of 40 randomly selected students at a major university. 18 22 13 15 24 24 20 19 19 12 16 25 14 19 21 23 25 18 18. 13 26 26 25 25 19. 17. 18 15 13 21 19 19. 14 24 20 21 23 22 19 17 If the university wants to accept the top 90% of the applicants, what should the minimum score be? A) 25 B) 26 C). 15 D) 14 22. Given the bar graph shown below, the Pareto chart that would best represent the data should have the bars in the following order. A) D A E C F B B) B F C E A D C) C A D E F B D) B F E D A C 23. Student Council President How many votes did Ann get? A) 80 B) 56 C) 128 D) 14 24. Calculate the mean of the following statistic studentsʹ test scores: 71 74 67 71 64 72 71 65 66 69 A). 71 B). 68 C). 69 D). 70 25. Calculate the median for the following sample: 5, 10, 6, 11, 1, 1, 10, 2,7 A). 6 B). 7 C) 10 D) 11 26. Calculate the mode for the following sample: 5, 10, 6, 100, 0, 0, 10, 0 A). 10. B) 5.5 C) 0 D) 16.25 27. The following data represent the bachelor degrees of CEOʹs at area small businesses. Determine the mode degree. Degree Number Accounting 29 Business 42 Liberal Arts 5 Marketing 24 Other 7 A) business B) accounting C) marketing D) no mode 28. The distribution of salaries of professional basketball players is skewed to the right. Which measure of central tendency would be the best measure to determine the location of the center of the distribution? A) median B) mode C) mean D) frequency 29. Compute the range for the set of data. 31, 23, 13, 14, 15, 16, 17, 9, 30 A) 4 B) 17 C) 22 D) 13 30. Find the sample standard deviation. 15, 16, 17, 18, 19 A) 2.5 B) 1.6 C) 1.3 D) 1.5 31. In the computation of the sample standard variance, how many degrees of freedom are there in a data set that has 15 data values? A) 16 B) 15 C) 14 D) none of these 32. A small computing center has found that the number of jobs submitted per day to its computers has a distribution that is approximately bell shaped, with a mean of 84 jobs and a standard deviation of 10. Where do we expect most (approximately 95%) of the distribution to fall? A) between 64 and 104 jobs per day B) between 74 and 94 jobs per day C) between 54 and 114 jobs per day D) between 64 and 114 jobs per day 33. Health care issues are receiving much attention in both academic and political arenas. A sociologist recently conducted a survey of citizens over 60 years of age whose net worth is too high to qualify for government health care but who have no private health insurance. The ages of 25 uninsured senior citizens were as follows: 68 73 66 76 86 74 61 89 65 90 69 92 76 62 81 63 68 81 70 73 60 87 75 64 82 Suppose the mean and standard deviation are 74.0 and 9.7, respectively. If we assume that the distribution of ages is bell shaped, what percentage of the respondents will be between 64.3 and 93.4 years old? A) approximately 83.9% B) approximately 68% C) approximately 95% D) approximately 81.5% 34. Fill in the blank. ____________ is a method of interpreting the standard deviation that applies to data that have a bell-shaped distribution. A) Chebyshevʹs rule B) The Empirical Rule C) Chebyshevʹs rule and the Empirical Rule D) none of these 35. For the following data, approximate the mean number of unused vacation days at the end of the year. Days Frequency 1-2 2 3-4 21 5-6 20 7-8 10 9-10 30 A) 6.6 B) 6.1 C) 7.1 D) 7.8 36. For the following data set, approximate the sample standard deviation of distances from work (in miles). Distance(miles) Frequency 8- 11 15 12- 15 21 16- 19 36 20- 23 39 24- 27 23 A) 4.9 miles B) 24.5 miles C) 5.2 miles D) 24.3 miles 37. Find the z- score for the value 96, when the mean is 92 and the standard deviation is 3. A) z = 1.00 B) z = 1.33 C) z = - 1.01 D) z = 1.01 38. Given the following five-number summary, find the IQR. 2.9, 5.7, 10.0, 13.2, 21.1. A) 18.2 B) 7.1 C) 11.1 D) 7.5 39. A) 0.819 B) 0.881 C) 0.990 D) 0.792 40. 41. Use the linear correlation coefficient given to determine the coefficient of determination, R2 r= 0.66 A). R2 = 81.24% B) R2 = 81.12% C) R2 =4.356% D) R2. = 43.56% 42. A) a B) b C). c D). d 43. 44. 45. The events A and B are mutually exclusive. If P(A) = 0.1 and P(B) = 0.5, what is P(A and B)? A) 0.5 B) 0.05 C) 0 D) 0.6 46. Assume that P(E) = 0.15 and P(F) = 0.48. If E and F are independent, find P(E and F). A) 0.072 `B) 0.15 C) 0.558 D) 0.630