What is population distribution?
The distribution of all the values of a variable in a population
What is a sampling distribution of the sample mean?
Distribution of the variable y*, for a variable y and a given sample size n
What is a sampling error?
The error resulting from using a sample to estimate a population characteristic
What is the relationship between sample size and sampling error?
The larger the sample size n (for a single sample):
The closer the sample means get to the population mean until, when n = N, y* = u
AND
The smaller the sampling error tends to be in estimating a population mean (u) by a sample mean (y*)
What is the mean of the sample mean?
For samples of size n, the mean of the sample means (i.e., the mean of the variable y*) equals the mean of the population or variable understudy
Mean (y*) = u
This means that the mean of all possible sample means equals the population mean
This holds true for any sample size n
What is the formula for calculation of the standard deviation of the sample mean?
SD = ay* = a/square root of n
This formula applies to:
Sampling with replacement from a finite population
Or, sampling from an infinite population (or very large population) with or without replacement
What happens to the standard deviation when the sample size gets larger?
The SD of the sample means gets smaller and smaller, until when n = N, the standard deviation of the sample mean = 0
What is the sampling distribution of the sample mean for a normally distributed variable?
If a variable y of a population is normally distributed with mean u and standard deviation a, then, for samples of size n (even if n is small):
- Shape: the sampling distribution of all possible sample means (known as variable y*) is also normally distributed
- Centre: the mean of the sampling distribution is: Mean(y*) = u
- Spread: the standard deviation of the sampling distribution is SD(y) = ay = a/square root of n
What is the central limit theorem (CLT)?
Regardless of the distribution of the variable under study, for a relatively large sample size, the variable y* is approximately normally distributed
The approximation becomes better with increasing sample size
What is the simple rule for relatively large sample size?
A sample size of 30 or more
(n greater than or equal to 30) is large enough
What is the independence assumption?
All the samples taken must be independently drawn from the population under study
What is the randomization condition?
In observational studies, samples must be randomly taken from the population
In experimental studies, all subjects must be randomly assigned to treatments
What is the sample size assumption and condition?
Large enough: sample size must be large (greater than 30 or 50), depending on the shape of the distribution of the population
10% condition (not large enough): when sampling without replacement, the sample size should be no more than 10% of the population, when sampling with replacement this condition is not required
What is the population proportion (p)?
The proportion (or percentage) of the entire population that has (or does not have) a specified attribute, p is a parameter
What is the sample proportion (p*)?
The proportion (or percentage) of a sample from the population that has (or does not have) a specified attribute
Is a statistic given by p* = y/n
