Transcript PANIC: The Method for Confidence Intervals

Christopher, Anna, and Casey




Normal distributions
Empirical Rule
Mean, standard deviation
Parameters and statistics

A level C confidence interval for a parameter
has 2 parts.
• A confidence level is calculated from the data, usually of
the form
Estimate +- margin of error

A confidence level C, which gives the
probability that the interval will capture the
true parameter value in repeated samples
[the success rate for our method]





P: Parameter of interest- Define it
A: Assumptions/conditions
N: Name the interval
I: Interval (confidence)
C: Conclude in context


Parameter: the statistical values of a
population (represented by a Greek letter)
Define in first step of confidence interval
 µ= the true mean summer luggage weight for
Frontier Airline passengers
1.
2.
The data comes from an SRS from the
population of interest.
The sampling distribution of x bar is
approximately normal. (Normality).
1. By central limit theorem if sample greater than 30
2. By graphing in your calculator if you have data
3.
Individual observations are independent;
when sampling without replacement, the
population size N is at least 10 times the
sample size n. (Independence).
1.
2.
3.
Given that the sample is random, assuming it
to be SRS.
Since n=100, the CLT ensures that the
sampling distribution is normally distributed.
The population of frontier airline passengers
is certainly greater than 1000, (10x100) so the
observations are independent.

Interval: T-interval for means


Formula
Plugged in from problem


Interval: (179.03,186.97)


We are 95% confident that the true mean
summer luggage weight of Frontier Airline
passengers is between 179.03 pounds and
186.97 pounds.
We are __% confident that the true mean
[context] lies between (____,____).









PHANTOMS
P: Parameter
H: Hypothesis
A: Assumptions
N: Name the test
T: Test
O: Obtain a p value
M: Make a decision
S: Summarize in context

µ= the true mean of perceived elapsed time
during a 45 second period by smokers who
haven’t smoked in the last 24 hours
Ho: null hypothesis- the claim we seek evidence
against
Ha: alternative hypothesis-the claim about the
population that we are trying to find evidence
for
 H µ=45
o:



Ha: µ 45
× = 59.3
Sx = 9.83
Assuming this sample to be an SRS of the
population.
2. The normal probability plot appears linear
indicating the population to be normally
distributed.
3. Independence N≥10n
N ≥(10)20
Surely there are more than 200 smokers in the
population.
1.



Test: One Sample T-Test
Significance level: alpha
α= .05 (1 - 95% =.05)
a)
b)
c)
Your t test statistic falls in the rejection
region
If the p value is less than your significance
level α
If the hypothesized parameter is not
captured in the confidence interval