```
library(tidyverse) # for data manipulation and data visualization
library(tidymodels) # for model fitting and to get residuals
```

# hw-4-instructions optional

## Introduction

For this homework assignment we will be exploring the Diamonds dataset. You will find this document which introduces `R`

commands necessary for this homework indispensable. Please review it thoroughly.

### Learning goals

In this assignment, you will…

- Find confidence intervals and perform hypothesis tests for proportions in
`R`

. - Interpret confidence intervals and hypothesis tests for the proportions.
- Fit a linear model to data in
`R`

. - Find and plot residuals in
`R`

.

## Getting started

### Log in to RStudio

Click on your *Stat1010.Rproj* that we made the first day of class.

Go to *File* ➛ *New File* ➛ *Quarto Document* and name the document *hw-4* click *create.*

## Packages

The following packages will be used in this assignment:

## Data: Diamonds

The diamonds dataset, from the `tidyverse()`

set of packages, contains information on 53,940 round diamonds from the Loose Diamonds Search Engine.

In

`R`

, compute a 97% confidence interval for the population proportion of diamonds that have an`Ideal`

`cut`

and interpret it in context.In

`R`

, test the hypothesis that the population proportion of`Fair`

diamonds is not equal to 3.5% and interpret it. Include all hypotheses, and the test statistic.In

`R`

, test the hypothesis that the population proportion of diamonds with`Very Good`

cut and the`best colour`

is equal to the population proportion of diamonds with`Premium`

cut and the`best colour`

. Include all hypotheses, and the test statistic, and interpret the test in context.Use

`R`

to fit a least squares line of best fit to predict the`price`

of a diamond using`x`

. Interpret \(b_0\), \(b_1\), and \(R^2\) in context, then plot the residuals and comment on the plot. Find the predicted value of price for \(x = 1.5\) and comment on the validity of this prediction. If a diamonds length increased by 5mm, our model predicts what increase in price?

Component | Points |
---|---|

1 | 2 |

2 | 4 |

3 | 3 |

4 | 10 |