Please read in the data using the following code and load the relevant libraries. The data is all the football game results from the 2023-24 football season. 

```{r}
nfl <- read.csv('https://vinnys-classes.github.io/spring/labs/nfl.csv')

head(nfl)
```


## Question 1

Among the other parts of the data is a column called FavDiff that is for a variable that is the difference in scores of the favorite vs underdog (unfavored to win) team. I'm wondering if the difference in score for the favorite and underdog is actually greater than 0 (ie the favorites score more points on average than the underdogs). To do this please run a t-test for one mean (the mean of FavDiff, the difference in scores for the favorite and underdog teams) to test this hypothesis.

#### Part 1 Please list your null and alternative hypothesis. 

#### Part 2 Please check the assumptions. 

Be sure to mention if the data was (randomly collect), if (the IID assumption holds), and if (the population is normal or n is large)


#### Part 3 Visualize your data

I advise using the hist() function which takes in a variable and creates a basic histogram. 

```{r}
#hist()
```

#### Part 4 Using R, please run the above t-test

Be sure to report the sample mean, the test statistic (the t value), degrees of freedom, p-value, and your decision. See the help page for the t-test function by running ?t.test if needed for the coding

```{r}

#t.test(data$variable,
#       mu = HYPOTHESIZED VALUE,
#       alternative = "DIRECCTION OF YOUR ALTERNATIVE")
          # choices are "greater", "less", or "two.sided"
      

```

#### Part 5 Confidence Interval

Report and interpret the 95% confidence interval from the above test




# Question 2

Let's try something else. Let's run a two sample t-test where we will check to see if the mean number of points for the favorite team is the same as the underdogs. 

#### Part 1 Please list your null and alternative hypothesis. 

#### Part 2 Please check the assumptions.

Be sure to mention if the data was (randomly collect), if (the IID assumption holds), and if (the population is normal or n is large for both groups). HINT: n for both underdogs and favorits is 544. I assisted by plotting the distributions for both subpopulations (favs and underdogs)

```{r}
hist(nfl$FavScore)
hist(nfl$DogScore)
```



#### Part 3

Using R, please run the above t-test.

Be sure to report the sample means and their difference, the test statistic (the t value), degrees of freedom, p-value, and your decision. See the help page for the t-test function by running ?t.test if needed for the coding

The below t test will check if variable 1 (from the dataframe called "data") has a greater mean than variable 2 (also from 'data')

```{r}
#t.test(data$variable_1,
#       data$variable_2,
#        alternative = 'greater')

```


#### Part 4

Please report a 90 percent confidence interval for the difference in the two means and it's interpretation. 90% is what we are after, the t.test funciton normally gives 95 so you'll have to figure out how to tweak the function.




#### Part 5 (Bonus Point)

This data is actually called "paired" in that each Favorite team has a corresponding Underdog team. As such, a "paired t-test" should be ran instead. Try it out by re-running the code from part 4 but change the parameter in the t.test() function called paired to TRUE. Compare this to your results in question 1