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21 Cards in this Set
- Front
- Back
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probability
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of any outcome of a random phenomenon is the proportion of times the outcome would occur in a very long series of repetitions.
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randomness
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if individual outcomes are uncertain but there is nonetheless a regular distribution of outcomes in a large number of repetitions
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sample space
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the set of all possible outcomes
S |
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probability rules
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rule 1: P(A) of any event A satisfies 0<P(A)<1
rule 2: if the S (the sample space) in a probability model, then P(S)=1 rule 3: Two events A and B are disjoint if they have no outcomes common and so can never occur together. If A and B are dis joint P(A or B)= P(A)+P(B) rule 4: additional rule to disjoint events. the complement rule states that P(A*)= 1-P(A) |
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multiplication rules for independent events
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two events A and B are independent if knowing that one occurs does not change the probability that the other occurs. If A and B are independent
P(A and B)= P(A)P(B) |
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random variable
discrete continuous |
a variable whose value is a numerical out come of a random phenomenon
has an finite number of possible values. every probability is a number between 0 and 1. P1+P2+....+Pk=1 takes all values in an interval of numbers, probability of any event is in the area under the density curve |
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disjoint events
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have no common outcomes
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independent events
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??
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mean and standard deviation of a sample mean
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mean of x-bar:
µxˉ = µ standard deviation of x-bar: σxˉ =σ/√n |
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central limit theorem
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when n is large, the sampling distribution of the sampling mean is normal.
X bar is approximately N( µ,σ/√n) |
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statistical inference
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a conclusion made on the basis of data which is subject to random variation of some kind
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confidence interval
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a level C confidence interval for a parameter is an interval computed from sample data by a meth that has probability C of producing an interval containing the true value of the parameter
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margins of error
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z* when confidence decreases margin of error decreases
n: when the sample size is smaller margin of error increases σ: when standard deviation increases the margin of error increases |
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null hypothesis
alternate hypothesis |
Ho:the statement being tested, usually no effect or no difference
Ha:true means are not the same |
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probability is less than alpha
probability is more than or equal to alpha |
reject Ho
fail to reject Ho |
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errors for hypothesis tests
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type 1: should have failed to reject
type 2: should have rejected |
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when we reject Ho
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we have enough evidence
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when we fail to reject Ho
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we do not have enough evidence
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assumptions for by hand
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simple random sample
standard deviation for population is given either the population is normally distributed or n is large enough |
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assumptions for on computer
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simple random sample
either the population is normally distributed or n is large enough. |
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standard error
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SExˉ =S/√n
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