Homework_1

Code

library(tidyverse)

── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
✔ dplyr     1.1.1     ✔ readr     2.1.4
✔ forcats   1.0.0     ✔ stringr   1.5.0
✔ ggplot2   3.4.2     ✔ tibble    3.2.1
✔ lubridate 1.9.2     ✔ tidyr     1.3.0
✔ purrr     1.0.1     
── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
✖ dplyr::filter() masks stats::filter()
✖ dplyr::lag()    masks stats::lag()
ℹ Use the ]8;;http://conflicted.r-lib.org/conflicted package]8;; to force all conflicts to become errors

Code

library(readxl)

dt <- read_excel("/Users/paritosh/Documents/Code_Submission/UMass/603_Spring_2023/posts/_data/LungCapData.xls")

Q.1)

A

Code

hist(dt$LungCap, freq = FALSE)

B

Code

dt %>% 
  select(Gender, LungCap) %>% 
  ggplot(aes(x = Gender, y = LungCap, fill = Gender)) + 
  geom_boxplot() +
  scale_y_continuous(breaks = seq(from = 0, to = 15, by = 0.75))

In median,quantiles and other measures males have higher lung capacity

C

Code

dt %>% 
  select(LungCap,Smoke) %>% 
  group_by(Smoke) %>% 
  summarise(mean = mean(LungCap))

# A tibble: 2 × 2
  Smoke  mean
  <chr> <dbl>
1 no     7.77
2 yes    8.65

Smokers have higher lung capacity. Ideally they should be having less as per out premise it does not seem to be the case, May be smoking might not be hurting the lung capacity as it is assumed to be.

D

• Age less than or equal to 13

Code

dt %>% 
  filter(Age <= 13) %>% 
  group_by(Smoke) %>% 
  summarise(LungCap = mean(LungCap))

# A tibble: 2 × 2
  Smoke LungCap
  <chr>   <dbl>
1 no       6.36
2 yes      7.20

• Age is equals 14 or 15

Code

dt %>% 
  filter(Age == 14 | Age == 15) %>% 
  group_by(Smoke) %>% 
  summarise(LungCap = mean(LungCap))

# A tibble: 2 × 2
  Smoke LungCap
  <chr>   <dbl>
1 no       9.14
2 yes      8.39

• Age is 16 or 17

Code

dt %>% 
  filter(Age == 16 | Age == 17) %>% 
  group_by(Smoke) %>% 
  summarise(LungCap = mean(LungCap))

# A tibble: 2 × 2
  Smoke LungCap
  <chr>   <dbl>
1 no      10.5 
2 yes      9.38

• Age is greater than or equal to 18

Code

dt %>% 
  filter(Age >= 18) %>% 
  group_by(Smoke) %>% 
  summarise(LungCap = mean(LungCap))

# A tibble: 2 × 2
  Smoke LungCap
  <chr>   <dbl>
1 no       11.1
2 yes      10.5

E

• After the age of 13 the lung capacity of non smokers is higher than that of smokers.

  Code

  # Creating a tibble
  table <- tibble( x = c(0,1,2,3,4), Frequency = c(128,434,160,64,24))
  n <- 810

Q.2)

A

Code

table %>%
  filter(x == 2) %>%
  pull(Frequency)/n

[1] 0.1975309

B

Code

table %>%
  filter(x < 2) %>%
  pull(Frequency) %>%
  sum()/n

[1] 0.6938272

C

Code

table %>%
  filter(x <= 2) %>%
  pull(Frequency) %>%
  sum()/n

[1] 0.891358

D

Code

table %>%
  filter(x > 2) %>%
  pull(Frequency) %>%
  sum()/n

[1] 0.108642

E

Code

table <- table %>%
  mutate(probability = Frequency / n) 

print(table)

# A tibble: 5 × 3
      x Frequency probability
  <dbl>     <dbl>       <dbl>
1     0       128      0.158 
2     1       434      0.536 
3     2       160      0.198 
4     3        64      0.0790
5     4        24      0.0296

Code

sum(table$x * table$probability)

[1] 1.28642

F

Code

 var(table$x)

[1] 2.5

Code

sd(table$x)

[1] 1.581139