POLS285 Test 2 Flashcards
What is the definition of probability?
Probability of an event occuring is the proportion of its occurrences over an infinite number of trials.
What is a random trial and random outcome?
-An action that produces a random outcome of interest (e.g, rolling a six-sided die).
-Random outcome: the result of a trial, e.g. rolling a one.
What is an event?
-A set of outcomes (could refer to any number of outcomes).
What are properties and rules of probability?
- All outcomes fall between 0 and 1.
-The sum of all possible outcomes (or the sample space) is always one.
-If event A and B are mutually exclivsive, the probability that either A or B occurs equals the probability that A occurs plus the probability that B occurs: P(A or B)=P (A) + P(B).
What is mutually exclusive?
-Probability of an action happening is mutual.
What is probability distribution and random variables?
-Random variable: Assigns a numeric value to each mutually exclusive event of a trial.
-Probability distribution: Identifies the possible events associated with a random variable along with their probabilities.
What are the properties of probability distribution?
1: Includes all possible events of a given random variable.
2:Identifies the probability of each event occuring.
3: Area under curve sums to 1.
What is the normal/Guassian distribution and what are its key properties?
-A probability distribution defined entirely by iys mean and standard deviation
-Key properties: Bell-shaped and Symmetrical.
-68-95-99 rule: 68% of observations within 1 standard deviation of the mean, 95% of observations within the second on e.
What is the significance of Gaussian distribution?
-Describes the distributions of some random variables in the natural and social worlds.
-But its real significance is its relationship with the central limit theorem.
-This relationship provides the foundation for inferential statistics,
and the subject of the next lecture.
What is statistical inference?
-Any descriptive or causal inference involves a target population: A group of units or cases we want to generalize to.
-But we’re usually stuck studying samples: a subset of population
units or cases selected for analysis and measurement.
-Statistical inference is the process of using information from samples to make probabilistic claims about target populations.
What is central limit theorem?
-Central limit theorem provides the mathmatical bridge to descriptive inference.
-States that if a random sample of n observations is drawn from a non-normal population, and if n is large enough, then the sampling distribution becomes approximately normal (bell shaped).
What does central limit theorum ask us to imagine and what is its relationship with sampling distribution?
- Have a target population (e.g. voting aged Canadians).
-Draw an infinite number of random samples from that population of the same size (or size n).
-Calculate the mean of a random variable for each sample e.g. Trudeaus mean thermometer score.
-Use those means to produce a sampling distribution or a distribution of the sample means.
What does the sampling distribution of central limit theorum look like and what is its central error?
- The means of the sampling distribution will be normally distributed.
- the mean of the sampling distribution will equal the true population mean μ.
- the standard deviation of the sampling distribution (or standard error) will equal the standard deviation of the variable divided by the square root of the sample size:
σ ̄y = σy√n
What are the different populations?
Target population: A group of units we want to generalize to.
Population parameter:
Sample statistics:
Census:
What is systematic sampling error?
-Affects the validity of our estimates.
-Occurs when sample statistics deviate from population parameters by chance.
-Key factors: sample size, population variance or heterogeneity.
-If non-systematic error is high, we say our estimates are unreliable
