Probability and Statistics - Tufts University
Terms
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- Hypothesis Test
- Hypothesize a value (or range of values) for the population characteristic, then asses whether the data supports that hypothesis
- Unbiasedness
- Expected value should be equal to the desired population parameter (E(stat) = population value)
- Efficiency
- Variability of stat should be small
- Confidence Interval Assumptions
- Assume Xi are random and independent
- Z or T Confidence Interval Reminders
- Use alpha/2
- Prediction Interval
- Predict a value for future observations of a random variable
- Tolerance Interval
- Example: 95% confident that 90% of resistors will be between...
- Null Hypothesis
- Hypothesis which is allowed to stand in the absence of convincing evidence
- Alternative Hypothesis
- Hypothesis which bears the "burden of proof"
- Type I Error, alpha
- Probability of falsely rejecting the null hypothesis given that the null is true
- Type II Error, beta
- Probability of failing to reject the null hypothesis, given that the alternative is true
- Operating Characteristic Curve (OC Curve)
- Plot of beta versus x-bar which is a graph of type II error
- Types of t-tests
- Pooled, 2-simple, Paired...for 2-simple, use the funky degrees of freedom equation
- Paired Test Pros and Cons
- Randomization - if there is a systematic difference in experimental technique, type I error could occur; Paired T is more sensitive, can discern real differences
- Conditions for using Paired T-Test
- Values must be associated by design, not arbitrarily; experiments designed in pairs, should be analyzed that way
- Study Rejection Regions for F-Test
- They are kind of funky...Section 9, Page 18
- What is (yi - y^i)?
- Residual
- Method of Least Squares
- Select b1 (slope) such that the sum of the squares of the residuals is a minimum
- Meaning of P on Exam Notes
- P is 2 for straight line