Study your flashcards anywhere!

Download the official Cram app for free >

  • Shuffle
    Toggle On
    Toggle Off
  • Alphabetize
    Toggle On
    Toggle Off
  • Front First
    Toggle On
    Toggle Off
  • Both Sides
    Toggle On
    Toggle Off
  • Read
    Toggle On
    Toggle Off

How to study your flashcards.

Right/Left arrow keys: Navigate between flashcards.right arrow keyleft arrow key

Up/Down arrow keys: Flip the card between the front and back.down keyup key

H key: Show hint (3rd side).h key

A key: Read text to speech.a key


Play button


Play button




Click to flip

16 Cards in this Set

  • Front
  • Back
Statistics inference
A process that we can get information and draw conclusion about the population from the sample
Estimate the parameters of the population using the statistics.
x_bar -> mu; s -> sigma
Point estimator (PE)
Draw inference for an unknown parameter about a single value or a point
Drawbacks about PE
(1) For continuous probability, P(x=a)=0 implies we hava zero prob. to have x_bar = mu, for example.
(2) Most of the time, we want how close the statistics to the parameters. PE cannot provides this info.
(3) As sample size (ss) increase PE won't be affect. As a good estimator, if ss increases, it will get more accurate.
Interval estimator
Draw inference for the unknown parameter about an interval.
i.e. within that interval, the parameter will be included with x% of confidence.
What is are good qualities for the estimator?
(1) unbiased
(2) consistency
(3) relatively efficiency
expected value of an estimator is equal to the parameter
as sample size increase, the difference btw an estimator and the parameter will be decrease
relative efficiency
If there are 2 unbiased estimator, the one with smaller variance is relative efficiency.
CI of mu, with CI = 1-alpha

interpret: the probability that mu as a fixed value included in the CI is 1-alpha
lower/upper CI limit
LCI = lower limit of CI
UCI = upper limit of CI
Useful z_a_over_2 values:

95%=? ...
1-a z_a_over_2
90% 1.645
95% 1.96
98% 2.33
99% 2.575
CI interpretation
About CI% of time for the repeatly sampling till infinity time that the true parameter is included within CI

Since in reality, we pick only one sample usually, our statistics and we only know that if we repeatly draw the samples we will have CI% of the samples contain the parameter
CI is affected by ___, ___, ___
(1) 1-alpha i.e. confidence level; inc->narrow
(2) n; inc->narrow
(3) sigma; inc-> wider
the wider CI is, the less precisous info it produces
sigma of sample median
= 1.2533sigma/root_n

=> bigger than sample mean, less relative efficiency
Sample size
If width of CI and CI% is specific, and sigma is given then

w = z_a_2*[sigma/root_n]
=> n=((z_a_2*sigma)/w)^2

Give sample size, we then can get a sample and find sample mean; Then, find CI.