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Research Notes
KEY (not always used, but used the same way) = Main Points       Key Words (get you points on tests)     Remember: these will save your life

1/31 � Chapter 10
Descriptive Statistics: Sum or Description of a population
Inferential Statistics: Generalization of populations from samples
Sample means (M) or proportions (P) allow us to infer a plausiblevalue of a characteristic

Confidence Intervals:

A sample gives us a statistic (sample M or P). We are unable to say exactly what the population mean or proportion is. To get around this we say we have a confidence that our parameter lies with in an interval. This interval is centered around a sample proportion (a mean). Basically its a point estimate with a margin of error we tack on, a Confidence Interval.

See book Definition for more info

Confidence Level (C): For every Confidence Interval there is a C

C is how much confidence" we have in our method. often choices for confidence levels are 90%, 95%, 99%.
Remember: A Confidence Level is not a probability
How to read a C: a C of 90% means
"in the long run, 90% of the results from this method will capture the true value of the population parameter being estimated within the confidence interval."

See book definition for more info

Applied: Confidence Interval for a pop. mean (we are currently using z-intervals)
To mix up a good C we work with three things
  1. SRS
  2. Pop. Mean (unknown)
  3. Standard deviation (won't have in reality, but have in current problems)
In order to use z-intervals we MUST have #'s 1 and 3.
A level C confidence interval of M is:
Z* (actual symbol) = Upper Critical Value of S.N.D. (z-distributions!)

Translated this means C is dervided from the SRS mean plus and minus Z* times the standard deviation  over the population2
Where as Z* is the positive value of the area to the left of one half the non confidence. A confidence of 99% leave 1% left over, half that is .005 - find that on the Z-Score box or witht he calc controls below and BAM you have your Z*!
How do we find the Z*? just use {2nd} {Distr} -> {3}(invNorm)  this gives -> invNorm(area to left)
Remember: book may write in interval notation: (98.1069,98.2991) Don't write this way! We write like this: 98.1009<M<2.9906
Here is a complete problem:

Text reads "always show work"
2/1 - Chapter 10
Steps for full credit on interval problems:
1. Name the Interval
Z-Interval for population mean
2. State and Check the conditions
      1. SRS
      2. Standard Deviation Known
      3. "Something about Norm Dist."
A) Given population distribution is approximately normal
B) Sampling Distribution is Approximately normal, n is large by the central limit theorem.
Remember: Do not use "it" when writing any of this!!!
3. Show the work
4. Write your final answer with the mean in between (_________<M<_________)
     How to Interpret a C
Pat Phrase (plug in your own data in the underline sections):
"I am 99% confident that the true mean number of years general managers spend with the company is between 11.01 and 12.59"

Creation date: Mar 8, 2010 5:44pm     Last modified date: Jun 22, 2014 9:05am   Last visit date: Jul 14, 2024 11:18am
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