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Statistics

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.

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Statistics

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  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. 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 179.03 pounds and 186.97 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

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