Man wants to run for election wants to know the chances of him winning
SD of Box can be used using the SD Shortcut Method
SD = Square Root (Fraction 1 x Fraction 2)
Example:
#Draws =2500
1328 favored candidate
Ave = .53
Ave not in Favor = .47
SD = SQRT(.53 x .47) = about .50
SE = (SQRT[2500] x SD) = 50 x .5 = 25
Chance error is 25 out of 2500
that is less than (25/2500) = 1%
He should run for election
Bootstrap
When sampling from a 0-1 box whose composition is unknow the SD of the box can be estimated by substitution the fractions of 0s and 1's in the sample for the unknown fractions in the box the estimate is good when the sample is reasonably large
Bootsrap method
25000 students registered students. Estimate sample of university students living at home.
Simple Random Sample of 400 students was drawn
317= were living at home
The sample percentage = 317/400 x 100% = 79% (estimate for population percent)
Next use the SD Shortcut to get the SD
SQRT(.79 x .21) = about .41
SE = SQRT(400) x SD = 20 x .41 = 8.2
Now convert to percent
(8.2/400) x 100% = 2%
Answer = 79% living at how with off by +-2%
Confident Interval
States that 2 SE will be within 95% of the total population. Think and the Normal Curve. 2 SD = 95% in area
1 interval sample percentage = +- 68%
2 interval sample percentage = +- 75%
3 interval sample percentage = +- 95%
how it could be bigger than 10 SE interval sample percentage. Remember area under curve never hits a 100%. There are no definete limits
Confidence Interval
(Using Normal Curve)
population = 25000
draw = 1600
917 people are democrats
Find a 95 Confidence interval
Find percentage = (916/1600) x 100% = 57%
Democrats = 57%
Other = 43%
Find SD = SQRT(.57 x .43) = 5
SE = SQRT(#draws) x sd = SQRT 1600 x .49 = 20
Covert into percent (20/1600) x 100% = 1.25
95% = +- 2SD
2 SD = 2 x 1.25 = 2.5
Answer = 57.3 +- 2.5 = Between 54.8% - 59.8%
Percentage formula
Number of 0s, 1s, SE/#draws x 100%
it just the fraction formula
Confidence interval Interpetation
A confidential interval is used when estimating an unknown parameter from sample data. The interval gives a range for the parament, and a confidence level that the range covers the true value
The chances are in the sampling procedure not in the parameters
The confidence level say that 95% of all samples, the interval +-2SE (in sample percents). The other 5% it does not cover
Chance Error and Confidence Interval
A sample will be off the population percentage due to chance error. The SE tells you the likely size of the amount off.
Warning to Confidence Interval and Sampling
Warning the formulas for simple random samples may not apply to other kinds of samples.
If the samples are not taken at random the square root law may not apply and may give silly answers.
Simple random samples is just about the same as drawing from a box with replacement -- the basis situation to which the square root law applies.