Quiz-6.utf8

title: “Quiz6” author: “Bryan McGrath” output: html_document: toc: yes editor_options: chunk_output_type: console —

For this quiz, you are going to use mpg (miles per galon) dataset. This dataset contains a subset of the fuel economy data that the EPA makes available on http: //fueleconomy.gov. It contains only models which had a new release every year between 1999 and 2008 - this was used as a proxy for the popularity of the car.

The dataset has the following variables:

manufacturer manufacturer name
model model name
displ engine displacement, in litres
year year of manufacture
cyl number of cylinders
trans type of transmission
drv the type of drive train, where f = front-wheel drive, r = rear wheel drive, 4 = 4wd
cty city miles per gallon
hwy highway miles per gallon
fl fuel type
class “type” of car

# Load the package
library(tidyverse)

## -- Attaching packages ------------------------------------ tidyverse 1.3.0 --

## v ggplot2 3.3.2     v purrr   0.3.4
## v tibble  3.0.3     v dplyr   1.0.2
## v tidyr   1.1.2     v stringr 1.4.0
## v readr   1.3.1     v forcats 0.5.0

## -- Conflicts --------------------------------------- tidyverse_conflicts() --
## x dplyr::filter() masks stats::filter()
## x dplyr::lag()    masks stats::lag()

# Import data
data(mpg, package="ggplot2")

# Print the first 6 rows
head(mpg)

## # A tibble: 6 x 11
##   manufacturer model displ  year   cyl trans      drv     cty   hwy fl    class 
##   <chr>        <chr> <dbl> <int> <int> <chr>      <chr> <int> <int> <chr> <chr> 
## 1 audi         a4      1.8  1999     4 auto(l5)   f        18    29 p     compa~
## 2 audi         a4      1.8  1999     4 manual(m5) f        21    29 p     compa~
## 3 audi         a4      2    2008     4 manual(m6) f        20    31 p     compa~
## 4 audi         a4      2    2008     4 auto(av)   f        21    30 p     compa~
## 5 audi         a4      2.8  1999     6 auto(l5)   f        16    26 p     compa~
## 6 audi         a4      2.8  1999     6 manual(m5) f        18    26 p     compa~

# Get a sense of the dataset
glimpse(mpg)

## Rows: 234
## Columns: 11
## $ manufacturer <chr> "audi", "audi", "audi", "audi", "audi", "audi", "audi"...
## $ model        <chr> "a4", "a4", "a4", "a4", "a4", "a4", "a4", "a4 quattro"...
## $ displ        <dbl> 1.8, 1.8, 2.0, 2.0, 2.8, 2.8, 3.1, 1.8, 1.8, 2.0, 2.0,...
## $ year         <int> 1999, 1999, 2008, 2008, 1999, 1999, 2008, 1999, 1999, ...
## $ cyl          <int> 4, 4, 4, 4, 6, 6, 6, 4, 4, 4, 4, 6, 6, 6, 6, 6, 6, 8, ...
## $ trans        <chr> "auto(l5)", "manual(m5)", "manual(m6)", "auto(av)", "a...
## $ drv          <chr> "f", "f", "f", "f", "f", "f", "f", "4", "4", "4", "4",...
## $ cty          <int> 18, 21, 20, 21, 16, 18, 18, 18, 16, 20, 19, 15, 17, 17...
## $ hwy          <int> 29, 29, 31, 30, 26, 26, 27, 26, 25, 28, 27, 25, 25, 25...
## $ fl           <chr> "p", "p", "p", "p", "p", "p", "p", "p", "p", "p", "p",...
## $ class        <chr> "compact", "compact", "compact", "compact", "compact",...

summary(mpg)

##  manufacturer          model               displ            year     
##  Length:234         Length:234         Min.   :1.600   Min.   :1999  
##  Class :character   Class :character   1st Qu.:2.400   1st Qu.:1999  
##  Mode  :character   Mode  :character   Median :3.300   Median :2004  
##                                        Mean   :3.472   Mean   :2004  
##                                        3rd Qu.:4.600   3rd Qu.:2008  
##                                        Max.   :7.000   Max.   :2008  
##       cyl           trans               drv                 cty       
##  Min.   :4.000   Length:234         Length:234         Min.   : 9.00  
##  1st Qu.:4.000   Class :character   Class :character   1st Qu.:14.00  
##  Median :6.000   Mode  :character   Mode  :character   Median :17.00  
##  Mean   :5.889                                         Mean   :16.86  
##  3rd Qu.:8.000                                         3rd Qu.:19.00  
##  Max.   :8.000                                         Max.   :35.00  
##       hwy             fl               class          
##  Min.   :12.00   Length:234         Length:234        
##  1st Qu.:18.00   Class :character   Class :character  
##  Median :24.00   Mode  :character   Mode  :character  
##  Mean   :23.44                                        
##  3rd Qu.:27.00                                        
##  Max.   :44.00

Q1-Q6 You believe that the typical car today drives at least 21 miles per galon (mpg) on highway. You have a sample of 234 cars. Test this hypothesis by answering Q1-Q6.

Q1 Calculate the standard error of the mean mgp on highway.

SEM <- sd(mpg$hwy) / sqrt(234)
SEM

## [1] 0.3892672

Q2 Calculate the sample mean.

Sample_Mean <- mean(mpg$hwy)
Sample_Mean

## [1] 23.44017

Q3 Calculate the upper and lower bound of the 95% confidence interval.

UpperCI <- Sample_Mean - 1.96 * SEM
UpperCI

## [1] 22.67721

Q4 Calculate the lower bound.

LowerCI <- Sample_Mean - 1.96 * SEM
LowerCI

## [1] 22.67721

Q5 Calculate the 95% confidence interval.

c(LowerCI, UpperCI)

## [1] 22.67721 22.67721

Q6 What is your conclusion regarding the hypothesis.

Given that at the start we predicted that a typical car drives about 21 miles per gallon and discovering that the lower bound, upper bound and sample mean are all over 21 miles per gallon we can conclude that our hypothesis was correct.

Q7 Now that you understand the mpg on highway, you want to test another hypothesis. You believe that the typical car today drives at least 16.5 miles per galon on city. To test this hypothesis, repeat Q1-Q6. Discuss your conclusion using the 95% confidence interval.

Hint: Inser the code below.

SEM <- sd(mpg$hwy) / sqrt(16.5)
SEM

## [1] 1.465932

Sample_Mean <- mean(mpg$hwy)
Sample_Mean

## [1] 23.44017

LowerCI <- Sample_Mean - 1.96 * SEM
LowerCI

## [1] 20.56694

c(LowerCI, UpperCI)

## [1] 20.56694 22.67721

Given the mpg of the on city is roughly 20 which is greater than 16.5 mpg proves that once again our hypothesis was correct.

Q8 Hide the messages and warnings, but display the code and its results on the webpage.

Hint: Use message, echo and results in the chunk options. Refer to the RMarkdown Reference Guide.