Symbols
- σ
- Population standard deviation.
- s
- Sample standard deviation.
- p
- Population proportion
- p̂
- Sample proportion
- x̄
- Sample mean
- μ
- Population mean
Terminology
- Hypothesis
- We start out assuming the H0 (the null hypothesis; always use =) is true.
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- Then we see if our sample shows us strong enough evidence for H1.
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- Parameters go in hypothesis (μ, p).
Overview
- x̄ is at the center of every confidence interval for μ.
- Confidence intervals build a range of guesses for a parameter.
- No information from the sample (no statistics) go in your hypothesis.
- Test statistics are the z or t values, p-value is given to the left.
- The p-value is the probability of observing the value of your statistic from the sample, or one more extreme, if the null hypothesis is true.
- For two-tailed p-values, multiply the probability in the closest tail by 2.
- One-tailed p-values: P(x̄ >= #) to P(z >= #) or P(t >= #).
- If the p-value is lower than α, reject H0 and conclude H1 is true.
Tailed Tests
- <
- Left-tailed test
- >
- Right-tailed test
- <>
- Two-tailed test
When to Use Statistics
One of:
- Sample size > 30 or normal distribution.
- np >= 10 in decimal form.
- np̂ > 10 in decimal form.
Errors
- If type 1 error (rejecting H0) is worse, choose an α value of 0.01.
- If a type 2 error (failing to reject H0) is worse, choose an α value or 0.10.
- Rejecting H0 may yield type 1 error.
- Failing to reject H0 may yield type 2 error.