`Ho`

This is your default assumption or belief.

`H1`

Notion that is **rival** to our default assumption or belief.

We attempt to test, statistically, whether `Ho`

is `True`

, or `False`

.

From our data analysis, we then proceed to either **not reject** or **reject** our `Ho`

. If we reject `Ho`

, we do so in favor of `H1`

; and vice-versa.

We can make mistakes while choosing to **reject** or **not reject**, however; and this is why we have `Type I`

and `Type II`

errors.

`Ho`

is `True`

If we

**do not reject**`Ho`

, then we are making the**correct decision**.If we

**reject**the null hypothesis, then we are making the`Type I`

error.

`Ho`

is `False`

If we

**reject**`Ho`

, then we are making the**correct decision**.If we

**do not reject**`Ho`

, then we are making the`Type II`

error.

We will employ the **Student's t-Test** to determine whether we should either **reject** or **not reject** `Ho`

.

Specifically, we will use the `t.test()`

function. Before diving in, let's take a look at a preview of docs:

```
?t.test
```

```
t.test {stats} R Documentation
Student's t-Test
Description
Performs one and two sample t-tests on vectors of data.
Usage
t.test(x, ...)
## Default S3 method:
t.test(x, y = NULL,
alternative = c("two.sided", "less", "greater"),
mu = 0, paired = FALSE, var.equal = FALSE,
conf.level = 0.95, ...)
...
```

Now let's mock a data set, called `test_data1`

. Next, we will compute its `t.test`

.

```
test_data1 <- c(55, 60, 62, 63, 65, 66, 68, 69, 70, 71, 75, 80)
t.test(test_data1)
```

```
One Sample t-test
data: test_data1
t = 34.357, df = 11, p-value = 1.522e-12
alternative hypothesis: true mean is not equal to 0
95 percent confidence interval:
62.70778 71.29222
sample estimates:
mean of x
67
```

Here, (having provided **no** further arguments) our `alternative hypothesis`

is such that the `true mean is not equal to 0`

. More elegantly:

`H1`

(alternative hypothesis) :`true mean is not equal to 0`

, therefore:`Ho`

(null hypothesis) :`true mean is equal to zero`

.

Since our **p-value** is less than `.05`

, we **reject** `Ho`

.

Therefore we are accepting our alternate hypothesis, which is that our true mean is not equal to 0.

- https://www.youtube.com/watch?v=RV8h9B4BV8k
- https://www.youtube.com/watch?v=scWZAcU8q_c

## COMMENTS