MATH 208 Final Exam Question 1 [50 points]

Description

data(midwest)

midwest_modified<-midwest %>% select(county,state,popdensity,

popwhite,popblack,

popamerindian,popasian,

popother,inmetro)

The data for this question comes from a modified version of the midwest dataset from the ggplot library.

str(midwest_modified)

tbl_df [437 x 9] (S3: tbl_df/tbl/data.frame)

	$ county		: chr [1:437] “ADAMS” “ALEXANDER” “BOND” “BOONE” …
	$ state		: chr [1:437] “IL” “IL” “IL” “IL” …
	$ popdensity		: num [1:437] 1271 759 681 1812 324 …
	$ popwhite		: int [1:437] 63917 7054 14477 29344 5264 35157 5298 16519 13384 146506 …
	$ popblack		: int [1:437] 1702 3496 429 127 547 50 1 111 16 16559 …
	$ popamerindian: int [1:437] 98 19 35 46 14 65 8 30 8 331 …
	$ popasian		: int [1:437] 249 48 16 150 5 195 15 61 23 8033 …
	$ popother		: int [1:437] 124 9 34 1139 6 221 0 84 6 1596 …
	$ inmetro		: int [1:437] 0 0 0 1 0 0 0 0 0 1 …
midwest_modified %>% slice(1:5) %>%
	select(county:popblack)
# A tibble: 5 x 5
	county	state popdensity popwhite popblack
	<chr>	<chr>		<dbl>	<int>	<int>
1	ADAMS	IL		1271.	63917	1702
2	ALEXANDER IL			759	7054	3496
3	BOND	IL		681.	14477	429
4	BOONE	IL		1812.	29344	127
5	BROWN	IL		324.	5264	547
midwest_modified %>% slice(1:5) %>%
	select(county,popamerindian:popother)
# A tibble: 5 x 4
	county	popamerindian popasian popother
	<chr>			<int>	<int>	<int>
1	ADAMS			98	249	124
2	ALEXANDER			19	48	9
3	BOND			35	16	34
4	BOONE			46	150	1139
5	BROWN			14	5	6

The dataset contains population data from midwest counties in five states in the United States from an unspecified year. There are identifying variables for both the county (the name) and the state (the postal abbreviation). The variable popdensity is a measure of density (population per unspecified area units). The variable inmetro is equal to 1 if the county is classified as a metropolitan area and 0 otherwise. The other variables contain counts of population size within self-identified racial classifications.

MATH 208 Final Exam December 18th – 21st, 2021

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MATH 208 Final Exam December 18th – 21st, 2021

• 1. [5 pts] Write a line of code that will generate the following tibble (or data.frame) containing the highest population density from each state:

• A tibble: 5 x 2 state Highest_Pop_Den

	<chr>	<dbl>
1	IL	88018.
2	IN	34659.
3	MI	60334.
4	OH	54313.
5	WI	63952.

• 2. [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:

• A tibble: 5 x 4

	county	state inmetro		Metro
	<chr>	<chr>	<int>	<chr>
1	ADAMS	IL	0	NonMetro
2	ALEXANDER	IL	0	NonMetro
3	BOND	IL	0	NonMetro
4	BOONE	IL	1	Metro
5	BROWN	IL	0	NonMetro

3. [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

• A tibble: 10 x 3

• Groups: state [5]

	state	Metro	Highest_Pop_Den
	<chr>	<chr>	<dbl>
1	IL	Metro	88018.
2	IL	NonMetro	2309.
3	IN	Metro	34659.
4	IN	NonMetro	3090.
5	MI	Metro	60334.
6	MI	NonMetro	2251.
7	OH	Metro	54313.
8	OH	NonMetro	5484.
9	WI	Metro	63952.
10	WI	NonMetro	2344.

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MATH 208 Final Exam December 18th – 21st, 2021

• 4. [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:

• A tibble: 5 x 3

• Groups: state [5] state Metro NonMetro

	<chr>	<dbl>	<dbl>
1	IL	88018.	2309.
2	IN	34659.	3090.
3	MI	60334.	2251.
4	OH	54313.	5484.
5	WI	63952.	2344.

Now we will work with only a modified version of the population counts for each county.

• 5. [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:

• A tibble: 5 x 3

	county	popdensity	HighDens
	<chr>	<dbl>	<chr>
1	ADAMS	1271.	NotHigh
2	ALEXANDER	759	NotHigh
3	BOND	681.	NotHigh
4	BOONE	1812.	High
5	BROWN	324.	NotHigh

Then we will compute the total number of people in each combination of state, inmetro and HighDens using the code below:

pop_xtabs<-xtabs(

I(popwhite+popblack+popamerindian+popasian+popother)~

state+Metro+HighDens,data=midwest_modified)

pop_xtabs

, , HighDens = High

Metro

state Metro NonMetro

IL 9323624 405933

IN 3728008 689565

MI 7697643 354081

OH 8811604 1078957

WI 3004347 386892

, , HighDens = NotHigh

	Metro
state	Metro NonMetro
IL	250175	1450870
IN	234438	892148
MI	0	1243573
OH	98555	857999
WI	326825	1173705

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MATH 208 Final Exam December 18th – 21st, 2021

6. [5 pts] What will the code pop_xtabs[“IL”,1,2] return as output?

6. [5 pts] Using only the pop_xtabs object above, write a line of code to find the total number of people in areas high density (i.e. HighDens is “High”) as below:

High NotHigh

35480654 6528288

8. [10 pts] Using only the pop_xtabs object above, write a line of code that computes the total population in the combination of State and HighDens to return the output below:

HighDens

state High NotHigh

IL 9729557 1701045

IN 4417573 1126586

MI 8051724 1243573

OH 9890561 956554

WI 3391239 1500530

1. [5 pts] Using only the pop_xtabs object above, write a line of code (or multiple lines of code) that computes the percentage of individuals in High and Low density in each state as below:

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

END OF QUESTION 1

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