Lecture 4.2 Sample estimation Flashcards
why do we draw a sample from a population?
cheaper and easier than measuring the entire population
what does a sampling strategy depend on?
the sample being representative of the population
what is a population?
group of individuals where we wish to measure a variable of interest
what is a population parameter?
summary values from populations e.g means ect
what is a sample?
subset of a population
whats an underlying assumption from a sample?
sample is drawn at random
values in the sample are independent
what does accuracy mean?
Free from bias
- sample means should be measured from the same samples within the same population
- results would ideally be centered around the true population mean
what does precision mean?
Repeat-ability
-sample means calculated from repeated samples of the same population and should show little variation
When is accuracy affected?
when we are affected in our ability to select a truly representative sample
when is precision affected?
depends on sample size and population variance
when is a statistic used to estimate a parameter unbiased?
mean of the sampling distribution is equal to the true value of the parameter being measured
what is the variability of a statistic ?
spread of its sampling distribution
what is a high bias?
spread away from the true value
what is high variability?
the data not being close together
how can you reduce variability and bias?
random sample
large sample size
what is the sample distribution?
frequency distribution of a statistic over an infinite samples of a given size from a population
what does the sample distribution represent?
how far the sample mean is from the population mean for any randomly selected sample
what does the sample distribution show as the sample size increases?
sample distribution of the mean should show a normal distribution
what is the standard error?
standard deviation of the sampling distribution
what does the standard error measure?
measures precision in terms of how much any sample statistic varies from one sample to another
why cant we usually determine the sampling distribution of the mean?
population is not known
what do we do as we cannot determine the sampling distribution?
Sample mean would estimate the unknown population mean
Sample standard deviation would estimate the standard error.
how is standard error calculated?
sample standard deviation dividied by the square root of the sample size
when will the mean of the sample distribution take the form of normal distribution?
large sample size n>30
irrespective of the distribution of the variable in the population
what does central limit theorem allow?
allows the sampling distribution of a statistic to be approximated from a sample
what two things affect the range of the confidence interval?
variation –> less variation means a smaller confidence interval
sample size –> larger sample size means a smaller confidence interval
what does a 95% confidence interval mean?
95% of repeated samples from this population will produce a plausible range of values which include the population parameter
what happens when the sample size is less than 30
central limit theorem is no longer valid
what is the student t-test and when do you use it?
when <30 samples
t-test applied with n-1 degrees of freedom (number of observations -1)
VARIABLE OF INTEREST MUST BE NORMALLY DISTRIBUTED IN THE POPULATION
