# Intro

Submitted By nbcoleman
Words 334
Pages 2
March 11, 2013
Introduction to Hypothesis Testing
1. Reminder: We have been finding probabilities related to given sample means based on given population means and standard deviations
A. Example: what is the probability of finding a sample mean that is further from the population mean than this sample mean is?
- maybe this sample actually came from a population with a DIFFERENT mean
- if so, we’d say the difference between our sample mean and population mean is
“significant” – i.e., not due to random chance
2. Formalizing this logic… Statistical hypotheses
A. The Null Hypothesis: H0
- states that there is NO difference between population means
- this is like saying that any difference in sample means is due to chance
- we always start by assuming this (like “innocent until proved guilty”)
B. The Alternative Hypothesis: H1
- states that there IS a difference between population means
- this is what we conclude when a difference is too unlikely to happen by chance
C. How unlikely is TOO unlikely?
- we set a cut-off point: the alpha level (α)
- the alpha level marks the extreme parts of the distribution: the critical region
- the critical region is usually the extreme 5%
- if the sample mean is in the critical region, we reject the null hypothesis (guilty)
- otherwise we accept the null hypothesis (not guilty)
3. Hypothesis testing with z-scores: scenario
A. Set-up:
- You know the mean and standard deviation of some population (Population A)
- You also have a sample mean
B. Does the sample come from a population with the same mean as Population A?
- H0: the population means are equal
- H1: the population means are not equal
C. Find the z-score of the sample mean
- is it in the critical region (the extreme 5%) of the distribution of sample means?
- if so, reject H0
4. Assumptions underlying hypothesis testing
A. Random sampling
B. Independent...

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