# Today’s agenda

## Today’s agenda

• Wrap up one variable inference

• Testing for independence

• Get started on App Ex 8

# Wrap up one variable inference

## Rent in Durham

Data from a random sample of 20 1+ bedroom apartments in Durham in 2012.

``durham_apts <- read.csv("https://stat.duke.edu/~mc301/data/durham_apts.csv")``

## Exploratory analysis

``````ggplot(data = durham_apts, aes(x = rent)) +
geom_dotplot()``````

``````durham_apts %>%
summarise(xbar = mean(rent), med = median(rent))``````
``````##    xbar med
## 1 920.1 887``````

## Load helper functions

``````source("https://stat.duke.edu/courses/Fall15/sta112.01/code/one_num_boot.R")
source("https://stat.duke.edu/courses/Fall15/sta112.01/code/one_num_test.R")``````

## Bootstrap CI for mean rent in Durham

Estimate the average rent in Durham for 1+ bedroom apartments using a 95% confidence interval.

``one_num_boot(durham_apts\$rent, statistic = mean, seed = 195729)``
``````## Summary stats: n = 20, sample mean = 920.1
## 95% CI: (795.968, 1044.232)``````

## Bootstrap CI for median rent in Durham

Estimate the median rent in Durham for 1+ bedroom apartments using a 95% confidence interval.

``one_num_boot(durham_apts\$rent, statistic = median, seed = 571035)``
``````## Summary stats: n = 20, sample median = 887
## 95% CI: (712.8174, 1061.1826)``````

## Bootstrap testing for a mean

• Construct the bootstrap distribution

• Shift it to be centered at the null value

• Calculate the p-value as usual: observed or more extreme outcome (more extreme in the direction of the null hypothesis) given that the null value is true

## Bootstrap test for average rent in Durham

Do these data provide convincing evidence that the average rent in Durham for 1+ bedroom apartments is greater than \$800?

``one_num_test(durham_apts\$rent, statistic = mean, null = 800, alt = "greater", seed = 28732)``
``````## H0: mu = 800
## HA: mu > 800
## Summary stats: n = 20, sample mean = 920.1
## p-value =  0.0251``````

## Other helper functions

For future use…

``````source("https://stat.duke.edu/courses/Fall15/sta112.01/code/one_cat_boot.R")
source("https://stat.duke.edu/courses/Fall15/sta112.01/code/one_cat_test.R")``````

# Testing for independence

## Is yawning contagious?

Do you think yawning is contagious?