$---$

title: "Hawks Analysis"

author: "Your Name"

date: $"2023-01-30"$

output:

word$\_$document: default

html$\_$document: default

$---$

$```\{$r message$=$FALSE, warning$=$FALSE$\}$

library$($table$1)$

library$($tolerance$)$

library$($infer$)$

library$($tidyverse$)$

$```$

$```\{$r include$=$FALSE$\}$

hawks.df $<-$ read.csv$("$Hawks$\_$subset.csv$")$

$```$

## Comparing Tail Span in Hawks

Data were collected on random samples of three different species of hawks, Sharp$-$shinned $($SS$)$ and Cooper's hawks $($CH$).$

## Question of Interest

# EDA

$```\{$r echo$=$FALSE, message$=$FALSE, warning$=$FALSE$\}$

table$1($ ~Tail $|$ Species, data $=$ hawks.df $)$

$```$

## Boxplot

$```\{$r echo$=$FALSE, message$=$FALSE, warning$=$FALSE$\}$

ggplot$($hawks$.$df$,$ aes$($x $=$ Species, y $=$ Tail, colour$=$Species$))+$

geom$\_$boxplot$()+$

labs$($title $=$ "Boxplot of Tail Span by Species",

subtitle $="($with mean symbol$)",$

caption $=$ "Your Name",

y $=$ "Tail Span",

x $=$ "Species"$)+$

stat$\_$summary$($fun$=$mean, geom$=$"point", shape$=20,$ size$=5,$ color$=$"darkblue", fill$=$"darkblue"$)+$

theme$($legend$.$position $=$ "none"$)$

$```$

# Confidence Interval and Hypothesis Test for the Difference in the Population Mean Tail Span

$```\{$r echo$=$FALSE, message$=$FALSE, warning$=$FALSE$\}$

t$.$test$($Tail ~ Species, mu$=0,$ conf.level $=0\mathrm{.}95,$

data $=$ hawks.df$)$

$```$

## Confidence Interval for the Difference in Population Median Tail Span

$```\{$r echo$=$FALSE, message$=$FALSE, warning$=$FALSE$\}$

wilcox.test$($Tail ~ Species, conf.int $=$ TRUE,

conf.level $=0\mathrm{.}95,$ data$=$ hawks.df$)$

$```$

## $95\%$ Bootstrap CI for the Difference in the Population Mean Tail Span

$```\{$r echo$=$FALSE, message$=$FALSE, warning$=$FALSE$\}$

Tail.boot $<-$ hawks.df $\%>\%$

specify$($response $=$ Tail, explanatory $=$ Species$)\%>\%$

generate$($reps $=1000,$ type $=$ "bootstrap"$)\%>\%$

calculate$($stat $=$ "diff in means",

order $=$ c$("$CH$","$SS$"))$

percentile$\_$ci $<-$ get$\_$ci$($Tail$.$boot$)$

Tail.boot $\%>\%$ visualize$()+$ shade$\_$confidence$\_$interval$($percentile$\_$ci$)+$

labs$($x$=$"Difference $($CH $-$ SS$)$ in Sample Mean Tail Span",

y$=$ "Frequency",

title$=$ "Hawk Analysis Bootstrap Distribution"$)$

$```$

$```\{$r echo$=$FALSE, message$=$FALSE, warning$=$FALSE$\}$

percentile$\_$ci $<-$ get$\_$ci$($Tail$.$boot$)$

percentile$\_$ci

$```$

## Tolerance Intervals

## CH Species

$```\{$r echo$=$FALSE, message$=$FALSE, warning$=$FALSE$\}$

CC$.$Tail $<-$ hawks.df $\%>\%$

filter$($Species $\%$in$\%"$CH$")\%>\%$

select$($Tail$)\%>\%$ drop$\_$na$($Tail$)\%>\%$ as$.$data.frame$()$

normtol.int$($CC$.$Tail$Tail,

alpha $=0\mathrm{.}05,$ P $=0\mathrm{.}95,$ side $=2)$

$```$

## SS Species

$```\{$r echo$=$FALSE, message$=$FALSE, warning$=$FALSE$\}$

SS$.$Tail $<-$ hawks.df $\%>\%$

filter$($Species $\%$in$\%"$SS$")\%>\%$

select$($Tail$)\%>\%$ drop$\_$na$($Tail$)\%>\%$ as$.$data.frame$()$

normtol.int$($SS$.$Tail$Tail,

alpha $=0\mathrm{.}05,$ P $=0\mathrm{.}95,$ side $=2)$

$```$