Download estimating with confidence 8.1 confidence intervals: the

Survey
yes no Was this document useful for you?
   Thank you for your participation!

* Your assessment is very important for improving the work of artificial intelligence, which forms the content of this project

Transcript
chapter 8: estimating with confidence
8.1 confidence intervals: the basics
I'm thinking of a number...
Activity p468 ­­
I have selected an integer, M. Rather than guess this integer, you will guess an interval of numbers that might include my integer.
The command "mean(randNorm(M, 20, 16))" selects a sample of 16 integers from the Normal distribution, N(M, 20). Based on this one sample mean, what is a good range that includes M? How confident are you of your interval?
Point estimate: single best guess for the value of a population parameter, i.e., the results of a survey or experiment, p­hat or x­bar
It is VERY UNLIKELY that our estimate is correct!! So, let's find a range of values that might include it.
Back to the activity, M = _____. If I keep taking samples of size 16, how often will my sample fall within a good range? What would be a good range? How confident can we be at different ranges? Let's investigate...
Confidence Interval:
estimate ± margin of error
Margin of error: how close the estimate tends to be to the true
parameter in repeated sampling
Confidence level, C: percent of time that our (unbiased) sampling
method would result in an interval that captures the true
parameter
confidenceinterval.html
The confidence level does
NOT tell us the chance
that a particular
confidence interval
captures the population
parameter.
Instead, the confidence interval gives us a
set of plausible values for the parameter.
CYU pg476
How much does the fat content of Brand X hot dogs vary? To find out, researchers measured the fat content (in grams) of a random sample of 10 Brand X hot dogs. A 95% confidence interval for the population standard deviation σ is 2.84 to 7.55.
1. Interpret the confidence interval.
1. We are 95% confident that the interval from 2.84 to 7.55 g captures the true standard deviation of the fat content of Brand X hot dogs.
2. Interpret the confidence level.
2. In 95% of all possible samples of 10 Brand X hot dogs, the resulting confidence interval would capture the true standard deviation.
3. True or false: The interval from 2.84 to 7.55 has a 95% chance of containing the actual population standard deviation σ. 3. False. The probability is either 1 (if the interval contains the true standard deviation) or 0 (if it doesn't).
Margin of Error = What this looks like for....
Sample means:
Sample proportions:
Consider the formulas...
How will the confidence interval (and margin of error) change as
n increases?
the confidence level (C) increases?
Gotta check conditions! We're assuming an approximately Normal
distribution, and we're sampling without replacing!
Attachments
confidenceinterval.html
confidenceinterval.jar
Document related concepts

German tank problem wikipedia, lookup

History of statistics wikipedia, lookup

Bootstrapping (statistics) wikipedia, lookup

Misuse of statistics wikipedia, lookup