final_exam_math208_2021_Q12_sols

WI 63951.67 5 rows b. [5 pts] Write a line of code that adds a new column to the midwest_modified tibble called Metro where the elements of that column are equal to a string “Metro” if inmetro is equal to 1 and “NonMetro” if inmetro is equal to 0. The first five rows are given below for the county , state , inmetro and Metro columns: county <chr> state <chr> inmetro <int> Metro <chr> ADAMS IL 0 NonMetro ALEXANDER IL 0 NonMetro BOND IL 0 NonMetro BOONE IL 1 Metro BROWN IL 0 NonMetro 5 rows Solution: midwest_modified<-midwest_modified %>% mutate(Metro=ifelse(inmetro==1,"Metro","NonMet ro")) head(midwest_modified %>% select(county, state,inmetro,Metro),5) county <chr> state <chr> inmetro <int> Metro <chr> ADAMS IL 0 NonMetro ALEXANDER IL 0 NonMetro BOND IL 0 NonMetro BOONE IL 1 Metro BROWN IL 0 NonMetro 5 rows c. [5 pts] Write a line of code that will generate the following tibble (or data.frame ) containing the highest population density from each state for metropolitan and non-metropolitan counties separately, using the modified tibble from part (b). dens_table

d. [5 pts] Assume the tibble from part (c) is called dens_table as above. Now write a line of code that produces a tibble which arranges the data above so that we have separate columns for “Metro” and “NonMetro”, as below: state <chr> Metro <dbl> NonMetro <dbl> IL 88018.40 2309.320 IN 34659.09 3090.375 MI 60333.91 2250.645 OH 54313.08 5484.214 WI 63951.67 2343.750 5 rows Solution: result_tibble<-dens_table %>% pivot_wider(id_cols=state,names_from=Metro, values_from=Highest_Pop_Den) head(result_tibble) state <chr> Metro <dbl> NonMetro <dbl> IL 88018.40 2309.320 IN 34659.09 3090.375 MI 60333.91 2250.645 OH 54313.08 5484.214 WI 63951.67 2343.750 5 rows Now we will work with only a modified version of the population counts for each county. e. [5 pts] Write a line of code to add a new variable to the data frame named HighDens which is equal to “High” if the population density for the county is higher than 1500 and “Not High” if the population density for the county is lower than 1500. Below are the first 5 rows of the data for the county , popdensity and HighDens columns: county <chr> popdensity <dbl> HighDens <chr> ADAMS 1270.9615 NotHigh ALEXANDER 759.0000 NotHigh

HighDens state High NotHigh IL 85.11850 14.881500 IN 79.67977 20.320233 MI 86.62148 13.378518 OH 91.18149 8.818511 WI 69.32541 30.674588 Solution: apply(pop_xtabs,c(1,3),sum)/apply(pop_xtabs,c(1),sum)*100 HighDens state High NotHigh IL 85.11850 14.881500 IN 79.67977 20.320233 MI 86.62148 13.378518 OH 91.18149 8.818511 WI 69.32541 30.674588 ##OR ## prop.table(apply(pop_xtabs,c(1,3),sum),1)*100 END OF QUESTION 1 Question 2 [50 points] We will re-use the same midwest_modified data that was used in Question 1, with all the modifications from the other question parts. The description is repeated below for your convenience. str(midwest_modified)

Identify these three plots by name: Plot 1 Plot 2 Plot 3 Solution: Plot 1: Histogram Plot 2: Density plot Plot 3: Boxplot b. [10 pts] Now we make the same plots, but for each state. Do you believe there is evidence of an association between state and population density? In particular, do we see di ff erences in the distributions of population density by state?

c. [4 pts] Which plot(s) do you think best shows the association between state and population density? Which plot(s) do you think does not shows the association between state and population density as clearly? Explain your answer and reasoning in a few sentences. Solution: The boxplots and histograms probably are the best. The boxplots show the di ff erences in central location better; the histograms show the di ff erences in spread and shape better. The density plot is less useful since it is very busy and it is influenced by the outliers. d. [5 pts] Which of the following plots could be used to assess the association between the popwhite and popblack variables? List all that apply (or say None if none would be appropriate). A. 2-d density plot B. Barplot C. Boxplot D. 2-d histogram Solution: A, D We now would like to make plots to take a di ff erent look at the population variables. Unfortunately, the format of the midwest_modified data needs to be further changed so that we can use it in a ggplot . e. [5 pts] Write a line of code that will create a new tibble converts the midwest_modified_new to “long” format where each row contains a population count for a specific racial group called Count , and the variable from where that count originated (e.g. popwhite ) as well as the state , county , and Metro information for that population group. You should not include the columns for HighDens , inmetro or popdensity . The first 10 rows of the new tibble are below midwest_modified_new %>% slice(1:10) county <chr> state <chr> Metro <chr> Race_Variable <chr> Count <dbl> ADAMS IL NonMetro popwhite 63917 ADAMS IL NonMetro popblack 1702 ADAMS IL NonMetro popamerindian 98 ADAMS IL NonMetro popasian 249 ADAMS IL NonMetro popother 124 ALEXANDER IL NonMetro popwhite 7054 ALEXANDER IL NonMetro popblack 3496 ALEXANDER IL NonMetro popamerindian 19 ALEXANDER IL NonMetro popasian 48 ALEXANDER IL NonMetro popother 9 1-10 of 10 rows Solution:

Metro popasian 538463 0.016085421 Metro popblack 4672825 0.139590573 Metro popother 668449 0.019968473 Metro popwhite 27496337 0.821393790 NonMetro popamerindian 50794 0.005952150 NonMetro popasian 34210 0.004008801 NonMetro popblack 144611 0.016945828 NonMetro popother 36402 0.004265665 NonMetro popwhite 8267706 0.968827556 1-10 of 10 rows Solution: metro_race_summaries<-midwest_modified_new %>% group_by(Metro,Race_Variable) %>% summarise(Race_Count = sum(Count)) %>% ungroup() %>% group_by(Metro) %>% mutate(Proportion=Race_Count/sum(Race_Count)) h. [5 pts] Using the tibble from (g), write a line of code that created the barplot below.