Stat_300_Fa23_Midterm_Exam (1)

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Stat 300 — Introduction to Probability and Statistics Midterm Exam ARC Fall 2023 Chima Sanchez Instructions This exam is designed to assess your learning in the first half of Stat 300 for the Fall 2023 semester. Please complete all questions, showing your work as needed. If you are asked to perform a calculation, show all work and/or explicitly state what functions you used on your TI-84 calculator. For all probability calculations, please express your answer as an exact fraction or decimal number rounded to four places after the decimal, as appropriate, for full credit. You are allowed to use your personal notes and a graphing calculator of your choice, but you may not use the textbook, consult the Internet, use a math helper app such as PhotoMath, use AI such as ChatGPT, or collaborate with others. This exam has 12 questions, totalling 100 points toward your midterm exam grade category. Honesty Statement Before you begin, please read the following academic honesty statement and sign as indi- cated on the line below. Failure to sign will result in a zero grade . I certify that I am submitting my own original work and did not receive assistance from others nor used any unauthorized aids. I understand that if I am found to have violated these rules, my exam grade is automatically assigned a zero and may be reported to the Office of Student Conduct. Signature Date 1

1. Describe the type of data and level of measurement in the variable given: the heights of 21–65 year-old women. 2. Please refer to the following scenario and Table 1: a study was performed by the American Medical Association to measure the effectiveness of a new software program designed to help stroke patients regain their problem-solving skills. Patients were asked to use the software program twice a day, once in the morning and once in the evening. The study observed 200 stroke patients recovering over a period of several weeks. Group Showed Improvement No Improvement Deterioration Used program 105 74 19 Did not use program 89 99 12 Table 1: Summarized data collected from stroke patients at end of study The study sought informed consent from the participants, in which they were warned of the risks of no improvement or deterioration in their condition, and subjects were selected for the treatment group by randomization. What kind of observational study or experimental design was used here? Be as descriptive as possible. 2 The variable "heights of 21-65-year-old women" is quantitative data as it involves numerical measurements and interval level of measurement as it allows for differences to be taken A prospective study involves collecting data moving forward from groups that share common factors (cohorts). This scenario, stroke patients were tracked over time as they used the software program, and their progress was observed to measure the impact of the intervention on their problem- solving skills. The study focused on observing the outcomes as the patients continued using the software over the study period, making it a prospective study or a cohort study.

3. Table 2 contains daily high temperatures for a Northern California town in the month of April: 61 61 62 64 66 67 67 67 68 69 70 70 70 71 71 72 74 74 74 75 75 75 76 76 77 78 78 79 79 95 Table 2: Daily high temperatures for a Northern California town in the month of April. Construct a relative frequency distribution for the data in Table 2 using a class width of 5 and first lower class limit of 60. 4. Table 3 contains the distances between 20 retail stores and a large distribution center. The distances are in miles. 29 37 38 40 58 67 68 69 76 86 87 95 96 96 99 106 112 127 145 150 Table 3: Distances (in miles) between 20 retail stores and a large distribution center. Calculate the mean ¯ x of these distances. Round to the nearest tenth of a mile. 3 class tally of temperatures frequency relative frequency 60-64 65-69 70-74 80-84 85-89 90-94 61, 61, 62, 64 66,67,67,67,68,69 70,70,70,71,71,72,74,74,74,75,75,75 none none 95 4 6 12 9 75-79 75,75,76,76,77,78,78,79,79 0 0 1 4/30 ≈0.133 6/30 ≈ 0.2 12.30 ≈ 0.4 9/30 ≈ .3 0 0 1/30 ≈ 0.0 add up all the distances = 1488 x =1488/20 =74.4 Rounded to the nearest tenth of a mile, the mean distance is 74.4 miles.

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