2. Point Estimate vs. Interval Estimate
⢠Statisticians use sample statistics to use estimate
population parameters. (i.e. Sample means are used to
estimate population means and sample proportions
are used to estimate population proportions)
⢠A population parameter can be conveyed in two ways
1. Point Estimate: a single number that is based on sample
data and represents a plausible value of the characteristic
p = # of successes in sample
n
2. Interval estimate: use of sample data to calculate an
interval of possible values of an unknown population
parameter
3. Confidence Intervals
⢠Confidence intervals are used to express the
precision and uncertainty associated with a
particular sampling method
⢠A confidence Interval (CI) consists of three
parts
1. Confidence Level
2. Statistics
3. Margin of Error
4. ⢠Confidence Level: describes the uncertainty of the sampling
method
⢠Statistics & Margin of Error describe the precision of the method
by defining an interval estimate
⢠Interval Estimate = sample statistic + margin of error
NOTE: confidence intervals are preferred to point estimates because confidence
intervals indicate precision and uncertainty of estimate
EX: Suppose we compute the interval estimate of the population parameter,
using a 90% confidence interval. This means if we use an identical sampling
method and choose different samples to compute different interval estimates,
the true population parameterâs range would be defined as: sample statistics
+ margin of error 90% of the time.
5. Confidence Level
⢠In confidence intervals, the confidence level (CL) plays the role
of the probability part.
⢠Describes the likelihood that a particular sampling method
will generate a Confidence Interval (CI) that includes the true
population parameter
⢠To interpret: If you collect all possible samples from each
given population and compute the confidence intervals for
each, then a 95% confidence interval means that 95% of the
interval includes the true population parameter.
6.
7. Margin of Error
⢠Margin of Error: the range of values above and below the
sample statistic in a confidence interval
⢠EX: If a survey is given to your student body and it reports
that 70% of students choose English as their favorite subject,
then you can state that the survey had a 10% margin of error
and confidence level of 90% which results in a confidence
interval of being 90% confident that English will receive
between 60% and 80% of the vote.
8. Bias/ Unbiased
⢠Bias: A preference or an inclination, especially
one that inhibits impartial judgment.
⢠Unbiased: having no bias or prejudice (being
fair or impartial)
⢠Of a sample: not affected by an irrelevant factors,
variables or selectivity which influence itâs distribution;
random
⢠Of an estimator: having an expected value equal to the
parameter being estimated
9. Review of Variability
⢠Variability: spread in a set of data that can be described by summary
measures through means of range, interquartile range, variance and
standard deviation
⢠Range: difference between largest and smallest values in a set of data
⢠IQR= Q3 âQ1
⢠Variance (Ď²) = ÎŁ( xi â Îź)
N
Standard Deviation (Ď) = â(Ď²)