Debrief Quiz #1

1. Debrief Quiz #1 Back to the Past

2. What’s it all about? People make statements – such-&-such is big, or small, or unusual, or common. We can’t help it; we like to describe what we see and what we think about what we see.

3. The Truth? How do we know that what we say – “such-&-such is big, or small, or unusual, or common – is reasonable? That depends, of course, on what we might mean by big, or small, or unusual, or common.

4. The truth depends How do we know that what we say – “such-&-such is big, or small, or unusual, or common – is reasonable? That depends, of course, on what we might mean by big, or small, or unusual, or common.

5. Formal versus Informal Inference Statistical Inference is formal – it is a set of prescribed methods using prescribed tools for extracting information from data. Informal Inference comes in various forms, such as stereotyping, and is representative things like snap judgments and bigotry. Remember the Journalist, the Scientist, and the Lawyer?

6. Statistics means never having to say you’re certain Statistics is a systematic way of quantifying uncertainty. – from very uncertain to reasonably (but not 100%) certain. Since we are using limited observations, i.e. samples, to make decisions, we must always be aware that the what we observe (our sample) might be an unlikely event, relative to the characteristics of what we study.

7. The Standard Normal Variate The “Z” statistic Many characteristics that we study exhibit central tendency is populations and symmetry in their dispersion around that central tendency. Central tendency and symmetrical deviation of it) makes the life of a Statistician less uncertain.

9. The Standard Normal Variate The “Z” statistic We find that the distribution of many characteristics can be described by their mean and standard deviation. And since we also see symmetry in σ around μ, we can create index on these two moments.

10. The “Z” statistic The Z-stat is an index that allows us to homogenize the distribution of any characteristic in a population and quantify the likelihood of any occurrence of that characteristic. An index is just a ratio. In our case, this ration will include three measures: X any randomly observed value μ the average of that characteristic σthe standard deviation of the characteristic

11. The “Z” statistic Zx = (x –μ) / σ This is the percentage in standard deviation of any observed deviation from the mean. • If x = the mean, then Zx is “0” for any distribution. • If x is a standard deviation from the mean, then Zx is “1” or “(1)” for any distribution.

12. If Zx= 1.5, then the P-value of x = Standard Deviations from the Mean

13. The Central Limit Theorem Dealing with Skew and Kurtosis by using Samples

14. The number of heads that occur in 1000 trials of 100 coin flips. = (50, 25) = (mean, SE)

15. Illustration The average weight of a Colorado skier/tourist is 190 pounds with a standard deviation of 25 pounds. Can we look at the probability of observing a skier/tourist who weighs more than 215 pounds?

16. Illustration 165 190 215 μ-25 μμ+25 The average weight of a Colorado skier/tourist is 190 pounds with a standard deviation of 25 pounds. Can we look at the probability of observing a skier/tourist who weighs more than 215 pounds?

17. 50% 34% 16% 215

18. Probability of a skier/tourist weighing between 190 and 200 pounds? 200 - 190 z = = 0.40 15.54% 25 x = 190 s=25 Weight 190200 z 0 0.40

20. What if the capacity of a Gondola that hold 50 people, 10,000 pounds? How confident can I be that I won’t have a problem? This is a slightly different question than what is the likelihood that I’ll encounter “a single” skier/tourist who weighs more than 200 pounds, i.e. 10,000 # capacity / 50 persons = 200 average Why?

21. Because the chances of getting one 200 # skier/tourist are greater than getting 50 200# skier/tourists.