Midterm 2 Flashcards
What is probability?
the science of chance behaviour (proportion of times an outcome will occur)
What is Gallup Polling?
random sampling gives information about
the sample (people polled) which can be used to make an
estimate of the population.
Is chance predictable?
Chance behaviour is unpredictable over the short run but is
regular and predictable over the long run.E.g. coin tossing
What is randomness?
A kind of order that emerges only after a long run.
What factors affect randomness?
Must have a long series of independent trials.
– Outcome of one trial must not influence the outcome of the next.
What is a probability model?
mathematical description of a random
phenomenon consisting of two parts – a sample space and
a method of assigning probabilities to events.
What is a discrete sample space?
Discrete variables that can
take on only certain values (a
whole number or a
descriptor). E.g. blood types
What is Continuous sample space?
Continuous variables that can take on any one of an
infinite number of possible values over an interval. E.g. cholesterol levels
What do all the probable outcomes sum to?
1
What is the equation for the probability of something not happening?
1 - the probability of it occuring
If two independent outcomes exist, what is the probability of either event occurring?
Probability of event 1 + probability of event 2
What is the addition probability rule?
Probability of an event is the sum of the probabilities of the
outcomes making up the event
What is Benford’s law?
Legitimate documents have a preponderance of 1s and 2s which
usually do not occur with falsified documents.
What is a Normal curve statistically speaking?
A Normal probability model
What is a random variable?
a variable whose numerical outcome is
due to a random phenomenon
What is probability distribution?
of X describes the values X can
take and how to assign probabilities to those values.
What are disjoint/mutually exclusive events?
events that NEVER happen together
What is the General Addition Rule?
pA+pB-P(a+b)
What are independent events?
One event has no probability change on the other
What is the Multiplication Rule for Independent Events?
Pa x Pb
What is sampling with replacement?
Experimental units are replaced before each new
sampling event is started – samples are independent.
What is conditional probability?
Conditional probabilities reflect how the probability of an
event can be different if we know that some other event
has occurred or is true.
What is a discrete random variable?
– random variables that have a
finite list of possibilities.
What is a continuous random variable?
infinite number of outcomes.
What is a risk?
The risk of an undesirable outcome of a random
phenomenon is the probability of that undesirable
outcome.
What is an odd?
The odds of any outcome of a random phenomenon is the
ratio of the probability of that outcome divided by the
probability of that outcome not occurring.
What is a parameter?
a number describing a characteristic of the population
What is a sample?
part of the population examined and for which we have data
What is the difference between mew and x (with a line over top)?
Mew = mean of the population
x + line = mean of a sample
What is important to remember about random sampling?
A statistic computed from a random sample is a
random variable.
What is a sampling distribution?
probability distribution of that statistic for samples
of a given size n taken from a given population.
What is the Law of large numbers?
As the number of samples of randomly sampled data increases, the mean of the sample gets closer to the population mean + the sample proportion gets closers to the population proportion
What is the Central limit theory?
When randomly sampling from any population
with mean µ and standard deviation σ, when n is large enough, the
sampling distribution of is approximately Normal: N(µ,σ/√n).
What is statistical inference?
Drawing conclusions from a sample about the population. Uses probability to state how reliable conclusions really are
Are sample means usually the same as the population mean?
No
What is a confidence interval?
The confidence interval is a range of values with an associated
probability or confidence level C. The probability quantifies the chance
that the interval contains the true population parameter
What are the two parts of a confidence interval?
estimate ± margin of error. Represent corresponding area under a curve
What does the confidence interval tell us?
with 95% confidence, we can say the population mean is two standard deviations away from the sample mean
What does the confidence level depend on?
z value
What does a large sample size mean?
Smaller standard deviation
What kind of error does the margin of error cover?
Random sampling error
For a legitimate experiment, what are some key rules for gathering samples?
The data must be a probability sample or come from a randomized
experiment
What is a confidence interval?
Confidence intervals are used to estimate a population
parameter, with a built-in estimate of the precision of that
estimate. Estimate ± Margin of Error. Relies on srs + central value theorem
What is statistical significance?
Statistical significance only says whether the effect
observed is likely to be due to chance alone because of
random sampling.
How does sample size affect statistical significance?
Because large random samples have small chance
variation, very small population effects can be highly
significant if the sample is large.
* Because small random samples have a lot of chance
variation, even large population effects can fail to be
significant if the sample is small.
What is the purpose of hypothesis testing?
Tests to see if sample data is valid with the hypothesis
What is a null hypothesis?
The null hypothesis is a very specific statement about a
parameter of the population(s). It is labeled H0
.
What is an alternate hypothesis?
The alternative hypothesis is a more general statement
about a parameter of the population(s) that is exclusive of
the null hypothesis. It is labeled Ha
Whats the difference between a one tail and two tail sided test?
Two sided has both null and alternative (one equals while other doesn’t equal). one sided has null and alternative (null and alternative is higher or lower)
How do you know which test to use?
If the question says higher or lower you only need to do a one sided test.
What is the p-value?
A way to confirm whether a null or alternative hypothesis is correct
What does a small p-value mean?
Small P-values are evidence AGAINST H0
. (less than 0.05)
What is a significance level?
Alpha. The largest p value tolerated for rejecting the null hypothesis. Decided before conducting the test
How can you find a confidence level in a two-sided test using alpha?
C= 1-a
What things must you know for a significance test?
Data is SRS, Normal, and standard deviation must be known
What is statistical power?
The power of a test of hypothesis with fixed significance level
α is the probability that the test will reject the null hypothesis
when the alternative is true.
In other words, power is the probability that the data gathered
in an experiment will be sufficient to reject an incorrect null
hypothesis.
What is a type 1 error?
when we incorrectly reject the null hypothesis
What is a type 2 error?
when we fail to reject the null hypothesis and it is false
What are conditions for inference around the mean?
A SRS
Normal distribution
Both mean and standard deviation are unknown
What is the difference between standard deviation and standard error?
SD=n-1 degrees of freedom
SE=mean +/- SE
