What Do samples tell us Chapter 3
Confidence Statement Has two parts
A margin of error and level of confidence. The margin of error says how close the sample statics lies to the population parameter. The level of confidence says what % of all possible samples satisfy the margin of error.
Variability
Describes how spread out the values of the sample statistic are when we take many samples. Large variability means that the result of sampling is not repeatable. A good sampling method has both small bias and small variability
Bias
Is a consistent, repeated deviation of the sample statistic from the population parameter in the same direction when we take many samples
Parameter
Is a number that describes the population. A parameter is fixed number, but in practice we don't know the actual value of this number
To reduce Bias
Use random sampling. When we start with a list of the entire population, simple random sampling produces unbiased estimates: The values of a statistic computed from a SRS neither consistently overestimate nor consistently underestimate the value of the population parameter.
What margin of error means
Margin of error plus or minus two percentage points is shorthand for this statement. " if we took many samples using the same method we used to get this one sample, 95% of the samples would give a result within plus or minus 2% points of the truth about the population"
Population size doesn't matter
The variability of a statistic from a random sample does not depend on the size of the population as long as the population is at lest 100 times larger than the sample.
To reduce the Variability of an SRS
Use larger sample. You can make the variability as small as you want by taking a larger enough sample.
Statics
is a number that describes a sample. The value of a statistic is known when we have taken a sample, but it can change from sample to sample. We often use a statistic to estimate an unknown parameter.
A quick method for the margin of error
use the sample proportion "P" from a SRS of size n to estimate an unknown n population proportion p. This margin of error of 95% confidence is roughly equals to 1/sqareroot number