Christopher, Anna, and Casey Statistics

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

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]

PANIC: The Method for Confidence Intervals

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

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

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).

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.

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

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

C: Conclude in Context 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 (____,____).

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

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

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

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.

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

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