STAT1008 Lecture Notes - Lecture 12: Stellar Population, Confidence Interval, Statistical Parameter
STAT1008 Week 4 Lecture C
● For practice for mid sem exam: Textbook questions, exam questions and review
content.
● Confidence Interval:
○ For a parameter is an interval computed from sample data for a method
that will capture the parameter for a specified proportion of all samples
○ When you compose many many samples some samples will include the
true parameter value and some will not
○ The success rate (proportion of all samples whose intervals contain the
parameter) is known as the confidence level
○ A 95% confidence interval will contain the true parameter of 95% of all
samples
○ Either or or situation
○ Green = contains the parameter values and red does not (POWERPOINT
EXAMPLE). Both fall within the range and gives a point estimate and a
sense of uncertainty aka where is the true population parameter
○ Parameter is fixed and doesn’t change for the population however the
statistic and interval is random (depends on sample).
○ 95% of these confidence intervals in the 95% confidence intervals will
capture the truth
○ Population -> single sample -> sample statistic -> repeat -> sampling
distribution -> standard deviation (standard error) -> margin of error
(2xSE) -> confidence interval
● Sampling Distribution:
○ Statistic + or - margin error
○ 95% of the data is in between two standard deviations of the centre
● 95% Confidence Interval:
○ If the sampling distribution is relatively symmetric and bell-shaped, a 95%
confidence interval can be estimated using statistic + or - 2xSE (standard
error = standard deviation for a special distribution which is your sampling
distribution)
○ If the percentage of the confidence interval changes the 2 changes in
value
○ 95% is the most used
● Interpreting a confidence interval:
find more resources at oneclass.com
find more resources at oneclass.com
Document Summary
For practice for mid sem exam: textbook questions, exam questions and review. For a parameter is an interval computed from sample data for a method that will capture the parameter for a specified proportion of all samples. When you compose many many samples some samples will include the true parameter value and some will not. The success rate (proportion of all samples whose intervals contain the parameter) is known as the confidence level. A 95% confidence interval will contain the true parameter of 95% of all samples. Green = contains the parameter values and red does not (powerpoint. Both fall within the range and gives a point estimate and a sense of uncertainty aka where is the true population parameter. Parameter is fixed and doesn"t change for the population however the statistic and interval is random (depends on sample). 95% of these confidence intervals in the 95% confidence intervals will capture the truth.