Download AP Statistics Notes 8.1 In this Activity, each team of three to four

AP Statistics
Notes 8.1
In this Activity, each team of three to four students will try to estimate the mystery value of the
population mean μ that your teacher entered before class.
Before class, Mrs. Prill will store a value of μ (represented by M) in the display calculator. With the
class watching, Mrs. Prill will execute the following command: mean(randNorm(M,2 0,16)). This tells
the calculator to choose an SRS of 16 observations from a Normal population with mean M and
standard deviation 20, and then compute the mean 𝑥̅ of those 16 sample values.
Point estimate: _________________________
Now for the challenge! Your group must determine an interval of reasonable values for the population
mean μ. Use the result from above and what you learned about the Normal distribution, 68-95-99.7%
rule, and sampling distributions. Share your team’s results with the class.
My group thinks that µ falls in the interval: ______________________________________________
Our rationale:
_____________ – 10 = ______________
_____________ + 10 = ______________
The interval ( __________ , __________ ) gives an
approximate 95% confidence interval for µ.
Confidence interval has 2 parts:
A confidence level C, which gives the overall success rate of the method for calculating the
confidence interval. That is, in C% of all possible samples, the method would yield an interval that
captures the true parameter value. (Most common is 95% confidence level)
WE WILL GET BETWEEN
0 INCHES AND 30
INCHES OF SNOW!
Interpreting Confidence Levels and Confidence Intervals
Confidence level: To say that we are 95% confident is shorthand for “95% of all possible samples of a
given size from this population will result in an interval that captures the unknown parameter.”
Confidence interval: To interpret a C% confidence interval for an unknown parameter, say, “We are
C% confident that the interval from_____ to _____ captures the parameter in context.”
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.
What’s the probability that our 95% confidence interval captures the parameter? It’s not 95%!
Before we take a sample that will be used to calculate a confidence interval, we have a 95% chance of
getting a sample mean that’s within 2𝜎𝑥̅ of the mystery μ, which would lead to a confidence interval
that captures μ. Once we have chosen a random sample, the sample mean 𝑥̅ either is or isn’t within
2𝜎𝑥̅ of μ. And the resulting confidence interval either does or doesn’t contain μ. After we construct a
confidence interval, the probability that it captures the population parameter is either 1 (it does) or 0 (it
doesn’t).
Example:
According to www.gallup.com, on August 13, 2010, the 95% confidence interval for the true
proportion of Americans who approved of the job Barack Obama was doing as president was 0.44 
0.03.
1. Interpret the confidence interval.
2. Interpret the confidence level.
3. True or false: The interval from 0.41 to 0.47 has a 95% chance of containing the actual
population standard deviation σ. Justify your answer.
Conditions for Constructing a Confidence Interval:
1. Random: The data come from a well-designed random sample or randomized experiment.
2. Normal: The sampling distribution of the statistic is approximately Normal.
3. Independent: Individual observations are independent. (10n ≤ population)
THESE THREE CONDITIONS (we will call them assumptions) MUST BE CHECKED AS PART
OF YOUR SOLUTION TO A PROBLEM.