Chapter 7 - The sampling distribution

sampling error

the error resulting from using a sample to estimate a population characteristic

sampling distribution of the sample mean

distribution of all possible sample means (all possible x̄ values) that can be obtained from a sample; for variable x and a given sample size, the distribution of the variable x̄

sampling error tends to be smaller for large samples then for smaller samples

possible sample means cluster more closely around the population mean as the sample size increase

mean of the sample mean

for samples of size n, mean of variables x̄ equals the mean of the variable under consideration

sample mean formula

μx̄ = μ

standard deviation of the sample mean

for samples of size n, the standard deviation of the variable x̄ equals the standard deviation of the variable under consideration divided by the sqrt of sample (gets small as sample size gets bigger)

standard deviation of sample formula

𝜎x̄ = σ /√n

1st step: get population standard deviation

2nd step: get standard deviation for samples with formula

larger the sample size, the smaller the sampling size tends to be

• larger the sample size, the smaller the standard deviation of x̄

• smaller 𝜎x̄ = the more closely the possible values of x̄ (possible sample means) cluster around mean of x̄

• mean of x̄ is the same as population mean