Hypothesis Testing

σ and Normality

Rough guidelines when and normality can't be assumed:

  1. If , our t-based confidence interval performs well in most practical situations
  2. If , our t-based confidence...

Hypothesis Testing

Two main types of statistical inference procedures:

  1. Confidence intervals
  2. Hypothesis tests

The topic of this chapter is: hypothesis testing for a population mean,

Hypothesis

Definition

The hypothesis is some claim about a population (i.e parameter), such as

Null Hypothesis

Definition

, the "current belief", conventional wisdom

Alternate Hypothesis

Definition

or , a challenge to

Left-tailed test:

Right-tailed test:

Two-tailed test:

Test Statistic

Info

we select the test statistic that allows us to calculate probabilities given is true

P-Value

Definition

The p-valuue is the probability of observing your evidence given is true

Method

[!steps]

Interpreting a P-Value

Note: is not a random statement (it is either true or it is not)

P-value: the probability of observing the evidence if is true

We compare the p-value to some arbitrary cutoff

Errors

These are known as "false positives" and "false negatives"

Type 1 Error

Definition

Type 2 Error

Definition

where is "power"

What the

https://media.tenor.com/p-69am5MkD8AAAAM/waffling.gif

In this course:

If you run a two-tailed hypothesis test, you can make a conclusion about the confidence interval

If you make a confidence interval, you can make a conclusion about a two-tailed hypothesis test