Exam II Review Flashcards
Classical approach
P(E) = Possible outcomes where E occurs / Total possible outcomes
Relative frequency approach
P(E) = Trials where E occurs / Total trials
Subjective approach
P(E) = Best guess
*Use when trials aren’t possible
Sample space
A collection or a set of possible outcomes of a random experiment
Unions
At least one of a number of possible events occurs.
A or B
Conjunctions
Two or more events all occur.
A and B
Marginal probability
The probability that a “simple” event will occur
Joint probability
The probability that two or more
events occur together
Conditional probability
The probability that an event occurs,
given that another event occurs
Independent events
The occurrence of A does not predict the occurrence of B. (And vise versa)
Testing for independence
Events A and B are independent if and only if
P(A|B) = P(A)
P(B|A) = P(B)
P(A and B) = P(A) x P(B)
If any one of these statements is true, the others are also true, and if any one of these statements is false, the others are also false.
Dependent events
The occurrence of one does help predict the occurrence of another
Inverse conditional probabilities
Generally, conditional probabilities cannot be inversed.
(As with most things, there are exceptions)
Discrete probability distribution
A list of all possible values of a discrete random variable X, with their respective probabilities
The list of outcomes is exhaustive.
The outcomes are mutually exclusive.
The probabilities sum to 1.
Continuous probability distribution
Have probability density functions (PDFs)
Parameter
Numerical descriptors of a population
Values usually unknown
Statistic
Numerical descriptors of a sample
Calculated from observations in the sample
Sampling error
Different samples will yield different values for the same statistic.
Different samples have different sample
means and standard deviations.
Sampling distributions
Probability distributions of multiple samples drawn from the same population that represent one sample statistic (such as mean or standard deviation)
Standard error
The standard error is a standard deviation, but the special name emphasizes that it’s the standard deviation of the sampling distribution.
Central Limit Theorem
As n increases, the distribution of
x-bar becomes normal and gets skinnier
Point estimates
A point estimate is a single number.
x-bar is a point estimate for μ.
A point estimate is unbiased if on average it
equals the thing we’re trying to estimate.
Interval estimates
An interval estimate for the population mean is a range of possible
values for μ.
Factors that affect CI width
Confidence level, sample size, and standard deviation of the population
Null hypothesis
An assertion that nothing is going on
Alternative hypothesis
Compliment of the null, usually is the claim we want to make
Significance level
Alpha level, used to conclude if we can reject the null hypothesis, chosen threshold for saying that the probability of xbar is small enough to reject the null hypothesis, usually .05.
Critical values
Correspond to the significance level
P-value
Probability associated with the observed result
Rejection-region approach
Does the test statistic exceed the critical value?
P-value approach
Is the p value less than the significance level?
Lowering the significance value _______ the critical values.
increases
Type I error
Rejecting the null when you shouldn’t
Type II error
Failing to reject the null when you should
Power
Probability of rejecting the null hypothesis, assuming that a specific alternative hypothesis is true
What affects power?
- Is it a one or two-tailed test (two-tailed yields lower power)
- As the difference between mu and mu0 increases, power increases
- As the sample size increases, the power for rejecting the null hypothesis increases.
t distribution
Used when population sd is unknown, not a normal curve like the z distribution
Looks like a standard normal distribution, but it is wider (it has thicker tails).
Degrees of freedom
The degrees of freedom are equal to the number of values that are “free to vary” once some information about them is already known.
For t tests, df = n-1
Effect size
A value measuring the strength of the relationship between two variables in a population, or a sample-based estimate of that quantity
