---
title: "Lab 7"
author: "Your Name Here"
date: ""
output: html_document
---

##### Remember to change the `author: ` field on this Rmd file to your own name.

### Learning objectives

> In today's Lab you will gain practice with the following concepts from today's class:

>- Using the **`t.test`** and **`wilcox.test`** commands to run 2-sample t-tests
- Interpreting the results of statistical significance tests
- Using **`qqnorm`** and **`qqline`** to construct normal quantile-quantile plots, and using them to assess whether data appear to be normally distributed
- Using **`fisher.test`** on 2x2 tables and interpreting the results

We'll begin by loading all the packages we might need.
```{r}
library(tidyverse)
Cars93 <- as_tibble(MASS::Cars93)
```

### Testing means between two groups

Here is a command that generates density plots of `MPG.highway` from the Cars93 data.  Separate densities are constructed for US and non-US vehicles.  

```{r}
qplot(data = Cars93, x = MPG.highway, 
      fill = Origin, geom = "density", alpha = I(0.5))
```

**(a)** Using the Cars93 data and the `t.test()` function, run a t-test to see if average `MPG.highway` is different between US and non-US vehicles.  *Interpret the results*

Try doing this both using the formula style input and the `x`, `y` style input.

```{r}
# Edit me
```

**(b)** What is the confidence interval for the difference?  Interpret this confidence interval.  

```{r}
# Edit me
```

**(c)** Repeat part (a) using the `wilcox.test()` function.

```{r}
# Edit me
```

**(d)** Are your results for (a) and (c) very different?  


### Is the data normal?

**(a)** Modify the density plot code provided in problem 1 to produce a plot with better axis labels.  Also add a title.

```{r}
# Edit me
```

**(b)** Does the data look to be normally distributed?  If not, describe why.

**(c)** Construct qqplots of `MPG.highway`, one plot for each `Origin` category.  Overlay a line on each plot as illustrated in lecture.

```{r}
# Edit me
```

**(d)** Does the data look to be normally distributed?  If not, describe why.

### Testing 2 x 2 tables

Doll and Hill's 1950 article studying the association between smoking and lung cancer contains one of the most important 2 x 2 tables in history.  

Here's their data:

```{r}
smoking <- as.table(rbind(c(688, 650), c(21, 59)))
dimnames(smoking) <- list(has.smoked = c("yes", "no"),
                    lung.cancer = c("yes","no"))
smoking
```

**(a)** Use `fisher.test()` to test if there's an association between smoking and lung cancer.

```{r}
# Edit me
```

**(b)** What is the odds ratio?  Interpret this quantity.

```{r}
# Edit me
```

**(c)** Are your findings statistically significant?  

```{r}
# Edit me
```

**(d)** Write an inline code chunk similar to the one you saw in class where you interpret the results of this hypothesis test.
