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

# HW 7 - Modern statistical inference (one group)

Due Monday, June 13, 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 (10 points)

- 9.2 – parts b and d (1 point)
- 9.4 (4 points) – Hint: use the symbol
`$`

to write mathematical equations; for instance, to write the fraction \(\frac{e^{\mu}}{\beta_0}\) simply use`$\frac{e^{\mu}}{\beta_0}$`

. - 9.8 (3 points)
- 24.8 – parts b-c with a
**percentile**bootstrap interval, the usual bootstrap interval that we have constructed in class (2 points)

For the remaining exercises, use the birth data set

## Confidence intervals via bootstrap (18 points)

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

the proportion of female newborn (6 points)

the mean weight of newborns (6 points)

the slope of

`gestation week`

in a simple linear regression model for`newborn_birth_weight`

(6 points)

## Hypothesis test via simulation (21 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 simulated samples and the significance level \(\alpha=0.05\) (5 points).

You want to determine whether exactly half of the newborns are female (7 points)

You want to determine whether the mean weight of newborns is 3500 grams (7 points)

You want to determine whether

`newborn_birth_weight`

is independent of`gestation week`

(7 points)

## Reproducibility (1 point)

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

before any code with a stochastic component.