STAT 164 - Introduction to Hypothesis Testing - CHAPTER 4.2

TEST OF HYPOTHESIS

also called significance testing, is a decision-making process for evaluating claims about a population by weighing between a set of educated guesses.

Statistical Hypothesis

a conjecture, speculation, or guess about an unknown population parameter which may be true or not

Null Hypothesis (H₀)

states that there is no difference between a parameter and a specific value or no difference between two or more populations

Null Hypothesis (H₀)

statement of equality or status-quo

= , ≥ , ≤

Alternative Hypothesis (H_a)

states the existence of a difference between a parameter and a specific value or difference between two or more populations

Alternative Hypothesis (H_a)

statement of inequality; sometimes referred to as the researcher’s hypothesis

≠ , < , >

What are the general steps of formulating a hypothesis?

• Type I error or P(Type I)

• Type II error or P(Type II)

LEVEL OF SIGNIFICANCE

• the maximum probability of committing a ___________ denoted by the Greek letter Alpha (α).

• This is one of the two errors committed during hypothesis testing together with the probability of committing a ____________ denoted by the Greek letter Beta (β)

Reject H₀, when H₀ is True 

Remember: RT

What is a type 1 error?

Fail To Reject H₀, when H₀ is False

Remember: FTRF

What is a type 2 error?

What is the Type 1 error in this scenario?

What is the Type 2 error in this scenario?

What is the Type 1 error in this scenario?

What is the Type 2 error in this scenario?

What is the Type 1 error in this scenario?

What is the Type 2 error in this scenario?

Test statistic

It is a function of a statistic computed from the sample compared to the hypothesized population parameter.

If the difference is significantly large, Ho is rejected. Otherwise, Ho is not rejected.