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 namemodel model namedispl engine displacement, in litresyear year of manufacturecyl number of cylinderstrans type of transmissiondrv the type of drive train, where f = front-wheel drive, r = rear wheel drive, 4 = 4wdcty city miles per gallonhwy highway miles per gallonfl fuel typeclass “type” of car# Load the package
library(tidyverse)
# 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, 2…
## $ year <int> 1999, 1999, 2008, 2008, 1999, 1999, 2008, 1999, 1999, 20…
## $ cyl <int> 4, 4, 4, 4, 6, 6, 6, 4, 4, 4, 4, 6, 6, 6, 6, 6, 6, 8, 8,…
## $ trans <chr> "auto(l5)", "manual(m5)", "manual(m6)", "auto(av)", "aut…
## $ 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. :44.00SEM <- sd(mpg$hwy) / sqrt(234)
SEM## [1] 0.3892672sample_mean <- mean(mpg$hwy)
sample_mean## [1] 23.44017upperCI <- sample_mean + 1.96 * SEM
upperCI## [1] 24.20313lowerCI <- sample_mean - 1.96 * SEM
lowerCI## [1] 22.67721c(lowerCI, upperCI)## [1] 22.67721 24.20313The conclusion regarding the hypothesis is that the calculated confidence interval is between the intervals of 22.667721 and 24.20313, but the hypothesis value for miles per gallon falls after at 25. The answer is that we are 95% positive that the hypothesis is wrong.
Hint: Inser the code below.
SEM <- sd(mpg$cty) / sqrt(234)
SEM## [1] 0.2782199sample_mean <- mean(mpg$cty)
sample_mean## [1] 16.85897upperCI <- sample_mean + 1.96 * SEM
upperCI## [1] 17.40429lowerCI <- sample_mean - 1.96 * SEM
lowerCI## [1] 16.31366c(lowerCI, upperCI)## [1] 16.31366 17.40429The conclusion of this hypothesis is that it is correct. The 95% confidence interval falls between 16.31366 and 17.40429 and suggests that we are 95% sure that the typical car gets at least 16 miles per gallon.
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