1. Christopher, Anna, and Casey
Statistics

2. What you should have learned: Math 1/ Math 2
Normal distributions
Empirical Rule
Mean, standard deviation
Parameters and statistics

3. Confidence Intervals: Overview
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]

4. PANIC: The Method for Confidence Intervals

5. PANIC P: Parameter of interest- Define it A: Assumptions/conditions
N: Name the interval
I: Interval (confidence)
C: Conclude in context

6. P: Parameters
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

7. A: Assumptions
The data comes from an SRS from the population of interest.
The sampling distribution of x bar is approximately normal. (Normality).
By central limit theorem if sample greater than 30
By graphing in your calculator if you have data
Individual observations are independent; when sampling without replacement, the population size N is at least 10 times the sample size n. (Independence).

8. Assumptions: (in context of problem)
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.

9. Interval: T-interval for means
N: Name Interval
Interval: T-interval for means

10. I: Interval
Formula
Plugged in from problem
Interval: (179.03,186.97)

11. C: Conclude in Context
We are 95% confident that the true mean summer luggage weight of Frontier Airline passengers is between pounds and pounds.
We are __% confident that the true mean [context] lies between (____,____).

12. Hypothesis Testing 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

13. P: Parameter
µ= the true mean of perceived elapsed time during a 45 second period by smokers who haven’t smoked in the last 24 hours

14. H: Hypothesis 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
Ho: µ=45
Ha: µ 45
× = 59.3
Sx = 9.83

15. A: Assumptions Assuming this sample to be an SRS of the population.
The normal probability plot appears linear indicating the population to be normally distributed.
Independence N≥10n
N ≥(10)20
Surely there are more than 200 smokers in the population.

16. N: Name the Test and Significance Level
Test: One Sample T-Test
Significance level: alpha
α= .05 (1 - 95% =.05)

17. Reject Ho if: 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