```
library(tidyverse)
library(infer)
hand <- read_csv("data/handedness.csv")
```

```
hand_prop <- hand %>%
count(handedness) %>%
mutate(proportion = n / sum(n)) %>%
pull(proportion)
hand_prop[1]
```

`## [1] 0.2077922`

The `handedness`

dataset contains a random sample of 77 Duke students with respect to their handedness status (one mixed-handed student was asked to choose which hand they primarily used to brush their teeth). It is documented that approximately 11 percent of the world is left-handed (Hardyck and Petrinovich, 1977 *Psychological Bulletin*). You are interested in whether Duke has a higher proportion of left-handed students than would be expected from the world average.

- Write out your null and alternative hypotheses in both words and symbols, being sure to define any notation used.

\[H_0: p = 0.11\] \[H_1: p > 0.11\]

\(H_0\) the proportion of students at Duke that are left-handed is equal to the world average of 0.11.

\(H_1\): the proportion of students at Duke that are left-handed is greater than the world average of 0.11.

- Conduct a simulation-based test of your hypotheses in Exercise 1, using 5,000 simulations (set a random seed of
`12345`

) and report your p-value.

```
set.seed(12345)
null_dist <- hand %>%
specify(response = handedness, success = "left") %>%
hypothesize(null = "point", p = .11) %>%
generate(reps = 5000, type = "simulate") %>%
calculate(stat = "prop")
```

```
null_dist %>%
visualise() +
shade_p_value(obs_stat = hand_prop[1], direction = "greater")
```

```
null_dist %>%
filter(stat >= hand_prop[1]) %>%
summarise(p_value = n() / nrow(null_dist))
```

```
null_dist %>%
get_p_value(obs_stat = hand_prop[1], direction = "greater")
```

- What do you conclude in the context of your research question?

Let \(\alpha = 0.01\).

Since the p-value is less than \(\alpha\), we reject the null hypothesis at the 0.01 significance level. We have enough strong enough evidence to suggest that the true population proportion of Duke students that are left-handed is not equal to 0.11 at the 0.01 significance level.

- Stage your modified files.
- Commit your changes with an informative message.
- Push your changes to your GitHub repo.
- Verify your files were updated on GitHub.