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Ch 1: Sampling Distribution (inferential statistics (techniques for making…
Ch 1: Sampling Distribution
inferential statistics
techniques for making statements about a population from a smaller population
generalizing a statement from the sample about the population
population
: the large set of observations we want to make an inference about
sample
: the smaller set of observations we use to make an inference
statistical inference
: when data collected form a random sample is generalized and applied to the population from which it was taken from
sample statistic
: the outcome score of a characteristic within a sample
random variable
bc it changes depending on the sample and it depends on chance that a particular characteristic is drawn during random sampling
sample space
: all possible outcomes in a sample
sample distribution
: the layout of outcome scores from many sample
histogram horizontal axis--> sample space
histogram vertical axis--> number of sample w/ particular value for the sample statistic
making a probability distribution from a sampling distribution: divide number of samples with sample statistics by the totally number of samples drawn
probability distribution
: a sampling space with probability (btwn 0 and 1) for each outcome of the sample statistic
discrete probability distribution
: when there is a limited number of outcomes possible in a probability distribution
information we get from a sampling distributions as a probability distribution
the outcomes we can expect (sample stats)
the probability that a particular outcome may occur based on the proportion of the sample statistic in the OG population
expected value
: the number we expect to extract from the sample distribution (mean of the sample distribution)
equal to proportion of population value if sample statistic is
unbiased estimator
of the parameter (pop. value)
balance point--> symmetric--> samples with less yellow candies the EV equally likely to be chosen as samples with more yellow candies
expected values of sample statistic equals true proportion of parameter if all sample stats are
unbiased estimators
of parameter.
downward bias
: estimation of a parameter based on sample statistic is underestimated (too low) bc pop is much larger than sample.
proportion in sample is unbiased estimator of population proportion
a sample is representative of a population if the variables in the sample are distributed the same way as in population
a random sample is not representative because of chance
we should expect it to be representative so we says that it is
in principle representative
of the population.
continuous variable
sample mean is the same as population mean if it is an unbiased estimator
p-values
= thresholds bc there is an infinite number of probabilities
probability density function
right handed and left handed
1.1