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Statistical Inference Drawing conclusions about the population from sample data Use probability to express strength of conclusions Statistical Inference assumes your data comes from a simple random sample or randomized experiment!!! Keep this idea in mind for your BIG project…
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Statistical Inference & CI's
Confidence Intervals Statistical Inference
Drawing conclusions about the population from sample data Use
probability to express strength of conclusions Statistical
Inference assumes your data comes from a simple random sample or
randomized experiment!!! Keep this idea in mind for your BIG
project Remember this? IF your data is normally distributed
68% of the data lies within 1 standard deviation of the mean. 95%
of the data lies within 2 standard deviations of the mean 99.7% of
the data lies within 3 standard deviations of the mean Little Lost
Gargamel wants to know the true mean of Smurf BMIs.
Smurf BMI: m = ? s = 13.72 Little Lost Gargamel wants to know the
true mean of Smurf BMIs. He takes a sample of size 30. His sample
mean= 21.6 He asks you to give him an interval where you are pretty
certain the whole smurf population falls Little Lost We know thatis
normally distributed thanks to the CENTRAL LIMIT THEOREM! Smurf
BMI: m = ? s = 13.72 Im a sample mean.68% of us are WITHIN a s
Where are you m?? 24.05? Where are you m?? 19.15? So Im going to go
hunting for m Where is my m? 2.45 2.45 Remember that 68% of the
results should be within 1 std dev of the mean I am 68% certain
that the population mean is between 19.15 and 24.05.
Watch Your Wording!!!! 68% of the intervals constructed with this
method would contain the population mean. I am 68% certain that the
population mean is between and Lets also look at how NOT to word it
68% of the time the population mean will be between 19.15 and
24.05
Watch Your Wording!!!! 68% of the time the population mean will be
between and 24.05 There is a 68% chance that the population mean is
between and 24.05 There is a 68% probability that the population
mean is between and 24.05 So How do I Make a Confidence Interval?
The Formula Standard Error How to get LESS margin of error
You find these in the t-table in the back cover of your book. Check
out the whiteboard for some sweet math action to find other z*s
This depends on how confident you want to be How to get LESS margin
of error Decrease confidence level Increase sample size What's the
Secret Ingredient?
I know the standard deviation of secret ingredient mix in the
Original Recipe Chicken Bucket is 3.5 oz. I want you to be 99%
confident and tell me what you think the overall mean ounceage is
In the sample of 100 buckets you asked me to look at, I found a
mean of 18.2 ouncesDoes that help? 17.2984 19.1016 = 3.5 and n =
100 So lets look at what we know
x-bar = z* = ? Z* = 2.576 So lets look at what we know Now, lets
get that interval Looks like we need a z* for 99% Confidence Whatd
You Find Pardner?
What's Your Report? Good Work, Geek!!! Whatd You Find Pardner?
Actually sir, What he meant to say was were 99% certain the mean
ounceage of secret ingredient is between and Aargh!!What a Moron!!
Well Sir, I believe theres a 99% chance the population mean falls
between ounces per bucket Finding Sample Size for a Desired Margin
of Error
Use the formula below if you want to find the sample size you need
to produce a specific margin of error A study of the career paths
of hotel managers taken from an SRS of 116 found the average time
they had spent with their current company was years.With a known
standard deviation of 3.2 years, how large of a sample would need
to be taken to estimate the mean within one year with 99%
confidence? We would need a sample size of at least 68. Where m is
the margin of error you are looking for!! Cautions for
Inference
Data must be from an SRS Inference has no correct method for
datacollected in a method different from SRS Outliers have a strong
effect on CIs Be sure to use the distribution of x-barbecause of
its normality For our current method, you MUST know The Final and
Biggest Warning!!!
A Few Last Warnings The margin of error in a CI covers random
sampling errors Difficulties from sample surveys and opinion polls
are often not covered in the margin of error 95% Confidence DOES
NOT say that there is a 95% probability that the true mean falls
within the interval. The True Meaning of a CI The numbers were
calculated by a method that gives correct results in 95% of all
samples. (you can say we are 95% confident or certain the mean is
within the interval) The Final and Biggest Warning!!! Using the
Calculator for CIs
Stat Tests 7: ZInterval - Stats Put in , x-bar, n, and C-Level *You
can also use a list of stats (Data) Calculate A random sample of 60
employees of a large corporation had a sample mean of 32.5 vacation
days with known standard deviation of 18.5 days.Find a 90%
confidence interval for the population mean of accumulated vacation
days. Homework #9,10,13,18-26