```
library(readr)
<- read_csv("https://rmorsomme.github.io/website/projects/training_set.csv") d
```

# HW 8 - Modern statistical inference (two groups)

Due Thursday, June 16, 9:00pm on Gradescope

This assignment needs to be completed with RMarkdown and submitted as a PDF on Gradescope. Feel free to re-use the template provided for HW1.

When submitting your work on Gradescope, please assign a page for each question.

## Problem set (23 points)

- 13.4 (4 points)
- 14.4 (2 points) – parts a and c
- 16.16 (1 point) – part e
- 16.20 (5 points)
- 16.22 (4 points)
- 16.24 (2 points)
- 16.28 (2.5 point)
- 16.30 (2.5 point)

For the remaining exercises, use the birth data set

## Confidence intervals via bootstrap (12 points)

Construct (5 points) and interpret in the context of the problem (1 point) a 95% confidence interval using 10000 bootstrap samples for

the difference in proportion of female newborns among women with and without risk factor (6 points)

the difference in the mean weight of newborns among women with and without risk factor (6 points)

## Hypothesis test via simulation (14 points)

Conduct a hypothesis test using simulation for the following cases. State the hypotheses in words and in mathematical symbols (2 points) and use 10000 samples simulated samples and the significance level \(\alpha=0.05\) (5 points).

You want to determine whether women with and without risk factor have the same proportion of female newborns (7 points)

You want to determine whether women with and without risk factor have newborns with the same mean weight (7 points)

## Reproducibility (1 point)

A seed is set with the command `set.seed`

before any code with a stochastic component.