Block 1 Activity (Lectures 1-3)

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Winona State University *

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110

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Statistics

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Feb 20, 2024

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Block 1 activity (Lectures 1-3) 1. The two boxplots below display final exam scores for all students in two different sections of the same course. A. Find the IQR of scores for the two sections. Section A Section B Approximate IQR 80 (120-40) 43 (100-57) B. Which section would you expect to have a larger standard deviation in scores, and why? Section A has a bigger section of IQR (spread and deviation measure) meaning it would make the most sense for Section A to have a larger standard deviation in scores. C. Indicate whether the following statement is true or false. If it true, provide justification. If it is false, correct the statement. “ Section A has a greater percent of students with scores at or above 80 than Section B .” Half of section A students scored 80 or above, same with section B. They are equal in percent at or above 80. D. Is it possible to tell which section has a greater percent of students with scores at or below 30? If so, find which section has the greater percent. If not, explain why this percent cannot be determined. The graph does not have anything marked below 40 in either section, so there’s no way of showing or determining scores below 30. E. A student in section A has a z-score of -0.5. Which of these is most likely that student’s score? Explain. i. 30 ii. 65 iii. 90 iv. 120

-0.5 is below the mean but not outstanding. It wouldn’t be 90 or 120 as they’re not below 80, and 30 is super low, so 65 makes the most sense. 2. The plot and table below summarize the relationship between sex and Instagram usage in a sample of 64 STAT 110 students: A. What are the observational units here? Students B. What are the two variables of interest? Explanatory variable: sex Explanatory variable type: categorical binary Response variable: Instagram use Response variable type: Categorical binary C. What percents should go in each cell of the mosaic plot? Cell A Cell B Cell C Cell D 92% (47/51) 8% (3/51) 61.5% (8/13) 38% (5/13)

D. If you wanted to describe the association between sex and Instagram usage, which two pairs of numbers could you compare to describe the association? You could compare the blues together or the reds together to describe association in the most sensible way. 3. The file Hospital.JMP contains information on 25 patients discharged from a Pennsylvania hospital. The data were collected as part of a study to investigate antibiotic usage in hospitals. The columns are:  ID: patient ID  Dur_stay: duration of hospital stay (in days)  Age  Sex  Temp; first body temperature following admission (in degrees F)  WBC; first white blood cell count (x10 3 ) following admission  Antibio; whether or not patient received antibiotic  Bact_cul; whether or not patient received bacterial culture  Service; whether patient received surgical or medical services A. Consider the association between sex and service type . i. Create a mosaic plot that summarizes this relationship. Make sure that the plot contains percents as well! ii. Copy-and-paste a screenshot of this plot. iii. Thoroughly describe the relationship between these two variables, following the guidance from Lecture 3.

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Females have a higher number of medical procedures over males, specifically 31.8% more likely. (550-18.2) B. Consider the relationship between type of service received and duration of hospital stay . i. Create side-by-side boxplots to summarize this relationship. ii. Find summary statistics (means, standard deviations, medians, quartiles) that can be used to compare these two groups. iii. Copy-and-paste a screenshot of this plot and the summary statistics. iv. Thoroughly describe the relationship between these two variables, following the guidance from Lecture 3. Medical procedures mean longer stays. Average stay for medical procedures is 11.1 days and for surgical 7.2. (11.1-7.2 is a 3.9-day difference between medical and surgical.) C. Consider the boxplots from part B. i. Which group (“medical” or “surgery”) appears to have the greater IQR? Explain. Medical procedures shows a wider box on the graph, making for a wider IQR.

ii. Using the summary statistics from part B, compute the two IQRs to confirm your intuition. Medical 9.5 (14-4.5) Surgical 4 (9-5) iii. Interpret the two IQRs. The median of the data is the IQR. 50% of patients were between 4.5 and 14 for medical and 5 and 9 for surgical. D. Once again, using your summary statistics from part B, answer the following. i. Suppose someone received medical service, and stays in the hospital for 15 days. Find the z-score corresponding to this measurement. Z score is .469 (15-11.1)/8.3 ii. Suppose someone received surgery, and stays in the hospital for 2 days. Find the z-score corresponding to this measurement. Z score is -1.7 (2-7.2)/3.1 iii. Which measurement is more unusual: the 15-day stay for a recipient of medical service, or the 2-day stay for the recipient of surgery? Explain your answer by comparing the two z-scores. -1.7 is further from 0 making it more unusual.