stats Final formal lab
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Concordia University Portland *
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Mathematics
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Feb 20, 2024
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MTH 243 StaTisTicS I FINAL FORMAL LAB NAME: This formal lab is an open-note, open-book, individual assignment. You cannot use online or software resources beyond the D2L course website and your calculator. However, you may work on this assignment with other students. Read all problems carefully. Please show all work and write clearly. Problems with work shown can receive partial credit. However, problems with little to no work can receive zero points. Indicate final answers with a box or circle. To submit your work properly, please follow the instructions found in the D2L Assignments page. INTRODUCTION: LINEAR CORRELATION IN COVID-19 DATA Below is a table of compiled data from various resources' regarding different demographic, economic, and social numbers from a sample of 10 US states along with their respective COVID-19 full vaccination rate and COVID-19 deaths per 100 (as of July 2022). COVID-19 COVID-19 Median Median % of house- % of house- Average US State Full vaccin- deaths per income ok holds with ~ holds with- house- ggfi?fi:g’ ation rate 100K in dollars? internet out vehicles hold size Alabama, 52.2 20047 51,734 39.0 76.8 6.10 2.55 2.6 California, 73T 937.04 80,440 36.5 86.9 7.11 2.95 3.9 Florida 68.9 79243 59,227 42.0 83.3 6.32 2.65 oy Kansas 63.2 89.47 62,087 36.7 82.2 5.39 2.51 3.7 Maryland 7.2 151.26 86,738 38.7 86.7 8.96 2.67 3.9 Montana, 58.1 34.9 57,153 39.9 81.5 4.97 2.39 2.7 Nevada 62.9 113.59 63,276 38.0 83.5 7.35 2.67 4.4 New York 8.1 701.63 72,108 38.8 83.2 29.06 2.59 4.4 Oregon 71.3 83.54 67,058 39.3 86.4 7.44 2:51 3.5 Washington 74.6 139.35 78,687 37.7 88.7 6.82 2.55 B Our main goal for this lab is to combine nearly everything we have learned in this course to construct a comprehensive statistical report of COVID-19 data in relation to certain economic, social, and demographic data points. 1Click on each variable in the table to directly go to the website each data set comes from. 2The median income, median age, % of households with internet, % of households without vehicles, and average household size data points for each state are all found on the same US Census Bureau COVID-19 website. Page 1 of 4 MTH 248 Statistics I Final Formal Lab
Ve 1. (§2.1-2.2, 15pts) First, we will analyze each data set individually to get an understanding of the a value, standard deviation, etc. of each variable. ’ a. Use Desmos or Google Sheets to compute the mean, standard deviation, and five-number summai of each column of the data table in the Introduction. That is, complete the table below. . COVID-19 COVID-19 Median Median % of house- % of house- Average Unemploy Full vaccin- deaths per income Age holds with holds with- house- me ;:npa.fc)z- ation rate 100K in dollars internet out vehicles hold size ner Std. dev. €537 _ = i & A . ? . = i I S 4 : 2, ' Min - s > ¢ p) .62 3 - . Q1 i 4 <, 163 % 3 ’ N - >p 12 L p . 7 Q2 »J ./ Lé | _ . ,, oL : Qs -~ Tl 7@ ~ - -~ -~ 'y e . 3 e - ; Max as1.0M0 gO755 A ‘ g C b. Then use Desmos or Google Sheets and the table from part a to compute the inter-quartile range and the upper and lower whiskers of each data set, and then determine if there are any outliers. That is, complete the table below. COVID-19 COVID-19 Median Median % of house- % of house- Average sl Full vaccin- deaths per income Age holds with holds with- house- mngxt fatz- ation rate 100K in dollars internet out vehicles hold size QR 4SO (D025 LUS ULWIFS 163 0,14 i uw g1, 16 > & ; ; ) £9 L8 1 , c& LW \(:C Q . /””T’ j AL O Outliers Ao nownwt WL g J ¥ 24 c. Finally, use Desmos (or hand draw) and the results from parts a and b to construct box plots for each data set. (COVID-19 Full vaccination rate, death per 100, median income, etc.) MTH 248 Statistics I Final Formal Lab Page 2 of 4
(-8.2, 25pts) Next, we will analyze the correlations between the state variables and the COVID-19 sccination rate and death per 100 by constructing scatterplots and performing some linear regression. a. Use Desmos or Google Sheets to construct a scatterplot and compute the best-fit least-squares line y = az + b for the COVID-19 Full vaccination rate vs. each state variable (median income, age, etc). Plot the best-fit lines with each scatterplot and report the 72 value. Label the axes of each scatterplot properly. Hint: there should be 6 scatterplots and best-fit lines. b. From your results in part a, which state variable (median income, age, etc.) has the highest corre- lation with the COVID-19 Full vaccination rate? c. Repeat parts a—b with the COVID-19 deaths per 100K vs. each state variable. ~ A . Ry } D ¢ < Page 3 of 4 MTH 248 Statistics I Final Formal Lab
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R NP 3. (88.1-8.2, 10pts) Finally, we will analyze the COVID-19 Full vaccination rate by state in terms of two categories: either a Democrat-controlled state legislature or a Republican-controlled state legislature. State legislature‘ control Republican | Alabama Florida Kansas Montana Democrat | California Maryland Nevada New York Oregon Washington Let state_leg denote the control of the state legislature of each state. If state_leg = 0, then it has a Republican-controlled state legislature. If state_leg = 1, then it has a Democrat-controlled state legislature. Use this table and notation to complete the following problems. a. Use Desmos or Google Sheets to construct a scatterplot of the COVID-19 Full vaccination rate vs. state_leg variable. Then find the best-fit line for this scatterplot. b. From your results in part a, what is the average vaccination rate in Republican-controlled states? And what is the average difference in vaccination rate between Republican- and Democrat-controlled states? MTH 248 Statistics I Final Formal Lab Page 4 of 4