---
title: "Bivariate Modeling Assignment"
author: "your name here"
format: html
execute:
  echo: true
  warning: false
  message: false
---


```{r}
# put the code to load any necessary R libraries and read in your cleaned data here. Delete this text afterward.
```


# (Q ~ B) Two sample T-Test for Independent Groups

1. **Identify response and explanatory variables**


2. **Visualize and summarise bivariate relationship** 


3. **Write the relationship you want to examine in the form of a research question.**

* Null Hypothesis: 
* Alternate Hypothesis: 

4. **Perform an appropriate statistical analysis.**
 
    a. 
Let $\mu_{1}$ be 

    b. 
$H_{0}: \mu_{1} - \mu_{2} = 0$  
$H_{A}: \mu_{1} - \mu_{2} \neq 0$ 


    c. 

    d. 


5. **Write a conclusion in context of the problem.**



\newpage

# (Q ~ C) Analysis of Variance


1. **Identify response and explanatory variables**


2. **Visualize and summarise bivariate relationship** 


3. **Write the relationship you want to examine in the form of a research question.**


4. **Perform an appropriate statistical analysis.**
 
    a. 
Let $\mu_{1}$ be the true mean
Let $\mu_{2}$ be the true mean
Let $\mu_{3}$ be the true mean

    b. 
$H_{0}: \mu_{1} = \mu_{2} = \mu_{3}$   
$H_{A}:$ At least one group mean is different. 


    c. 


    d. 


5. **Write a conclusion in context of the problem.**



\newpage 
 
# (B ~ C) Chi-Square test of Association

1. **Identify response and explanatory variables**


2. **Visualize and summarise bivariate relationship** 


3. **Write the relationship you want to examine in the form of a research question.**


4. **Perform an appropriate statistical analysis.**
 
    a. 
Let $p_{i}$ be the true proportion of 

    b. 
$H_{0}: p_{1} = p_{2} = p_{3}$   
$H_{A}:$ At least one proportion is different. 

  

    c. 


    d. 


5. **Write a conclusion in context of the problem.**



\newpage
 
# (Q ~ Q) Linear Regression Analysis



1. **Identify response and explanatory variables**


2. **Visualize and summarise bivariate relationship** 


3. **Write the relationship you want to examine in the form of a research question.**


4. **Perform an appropriate statistical analysis.**
 
    a. 
Let $\beta_{1}$ be 

    b. 
$H_{0}: \beta_{1} = 0$   
$H_{A}: \beta_{1} \neq 0$   


    c. 


    d. 


5. **Write a conclusion in context of the problem.**

