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CHAPTER 7 - SAMPLING AND SAMPLING DISTRIBUTIONS - Coggle Diagram
CHAPTER 7 - SAMPLING AND SAMPLING DISTRIBUTIONS
PARAMETERS
the numerical characteristics of a population
SAMPLING DISTRIBUTION
sampling distribution of x bar is the probability distribution of the sample mean
the probability distribution of all possible values of the sample mean xbar is the sampling distribution of xbar
a probability distribution for all possible values of a sample statistic is known as a sampling distribution
a simple random sample of size n from an infinite population of size N is to be selected. each possible sample should have the same probability of being selected
STANDARD ERROR
SE = standard deviation / square root of the sample size
as the sample size increases the standard error of the mean decreases
CENTRAL LIMIT THEOREM
if you take sufficiently large random samples from any population (regardless of the populations shape) the distribution of the sample means will be approximately normally distributed
key points
shape
the sampling distribution of sample means (xbar) will be approximately normal (bell shaped)
centre
the mean of the sampling distribution equals the population mean
spread
the standard deviation of the sampling distribution (called standard error) equals σxˉ=σ/square root n
PROBABILITY DISTRIBUTION
the probability distribution of all possible values of the sample proportion pbar is the sampling distribution of pbar
PRACTISE QUESTIONS
.A population consists of 500 elements. We want to draw a simple random sample of 50 elements from
this population. On the first selection, the probability of an element being selected is
a. 0.100
b. 0.010
c. 0.001
d. 0.002
on the first selection - equal chance of being selected - probability = number of elements to select / total number of elements = 1/ 500 = 0.002
SAMPLE MEAN
the closer the sample mean is to the population mean the smaller the sampling error
the sample mean can be smaller, larger or equal to the population mean regardless that the sample size is always smaller than the size of the population
POINT ESTIMATION
in point estimation data from the sample is used to estimate the population parameter
the sample statistic s is the point estimator of σ
the sample mean is the point estimator of μ
SAMPLING
the expected value of xbar is the mean
as the sample size becomes larger the sampling distribution of the sample mean approaches a normal distribution
whenever the population has a normal probability distribution the sampling distribution of xbar is a normal probability distribution for any sample size
the sampling error is the difference between the value of the sample mean and the value of the population mean
the standard deviation of a sample of 100 elements taken from a very large population is determined to be 60 the variance of the population can be any value greater or equal to zero
a convenience sampling method does not lead to probability samples
the standard deviation of a point estimator is called the standard error
a theorem that allows us to use the normal probability distribution to approximate the sampling distribution of sample means and sample proportions whenever the sample size is large is known as the central limit theorem
the number of random samples without replacement is calculated by
INFERENCE
s is a point estimator
a population characteristic such as a population mean is called a parameter
a sample statistic such as a sample lean is known as a statistic
a single numerical value used as an estimate of a population parameter is known as a point estimate
the sample statistic such as xbar, s or pbar that provides the point estimate of the population parameter is known as a point estimator
the purpose of statistical inference is to provide information about the population based upon information contained in the sample
