STAT 120

Bastola

Core intro stats covered: EDA for data comprehension, estimation with confidence, and hypothesis testing via p-values.

Upcoming focus: Advanced inference methods, transitioning from simulations to probability models for bootstrap/randomization distributions.

A density curve is a theoretical model to describe a distribution.

Distribution for

- individual measurements in population (for a quantitative variable)
- Sampling distribution for a statistic

All density curves have an area under the curve of 1 (100%)

- give proportions/percents as areas under the curve

A normal distribution has a symmetric bell-shaped density curve.

The mean and SD determine how a normal density curve looks. The normal model parameters are

- \(\mu\) = model mean (center)
- \(\sigma=\) model SD (variability)

- The curve represents the normal distribution, denoted by \(N(\mu, \sigma)\).
- (CALCULUS!!) Calculating the exact area requires integration, as given by the formula: Area \(=\int_a^b \frac{1}{\sqrt{2 \pi \sigma}} e^{-\frac{(x-\mu)^2}{2 \sigma^2}} d x\)
- We’ll just utilize technological tools.

What percent of the population scored 650 or higher?

`[1] 0.1586553`

`[1] 0.1586553`

What score is the \(25^{th}\) percentile?

When have we already been using normal models??

- Bootstrap distributions – get confidence intervals if a bootstrap distribution is roughly bell-shaped
- Randomization distributions – many of these are bell-shaped.
- Normal models play a huge role in statistical inference.
- If we know the (bootstrap/randomization) standard error then we can just use a normal model rather than a resampling model (which requires more computational effort)

- Please download the Class-Activity-15 template from moodle and go to class helper web page

`30:00`