Transcript Document
Michael Shadbolt Otumoetai College [email protected] Introduction Otumoetai College, State Co-ed in Tauranga. 2000 students. 2IC Math Dept. 8 years teaching. L3 Statistics for most of that. Standards realignment, full L2 Statistics course (no standards in common with our L2 Math course.) As a result, we now have five L3 Statistics classes, without taking numbers away from the three L3 Calculus classes. Q1. Why can incorrect Bivariate analysis kill puppies? Puppy Lives? You Decide! It’s not always obvious which variable is the response and which is the explanatory. Sometimes we need to think about which one makes more sense as an explanatory. Eg: Heart weights of puppies vs body weights of puppies. Do we want to be able to predict a puppy’s body weight by cutting out its heart and weighing it? Or do we want to be able to predict a puppy’s heart weight by weighing the whole puppy? In this case, perhaps it would be better if heart weight was response and body weight was explanatory… I ruff you! Q2. Why is freeze-dried ice-cream better than cornflakes? Continuity Correction Question: The weight of boxes of “Kellogg’s Kream Krunch” are normally distributed with a mean of 760g and a standard deviation of 5g. If the weight of the boxes is recorded to the nearest gram, find the probability that a box of “Kream Krunch” is recorded as at least 750g. Answer: If the box is to be recorded as at least 750g, the actual box must exceed 749.5g Thus P(X ≥ 750) = P(X > 749.5)(continuity correction) = 0.98213 (note: without continuity correction, the answer would have been 0.97724) Q3. Why is goody-gumdrop ice-cream "poissonous"? You Scream, I Scream… • • • You will be given a scoop of gumdrop ice cream. Eat it and count the number of pieces of gumdrop you get. The random variable X will be the number of pieces of gumdrop per scoop of ice cream. Q4. Why is Yoda a fan of Venn Diagrams? P(Try′) = 1 P(Do) = 0.7 P(Do′) = 0.3 P(Try) = Ø 0.3 P(Do) 0.7 P(Try) ? Q5. Am I going to die from a meteor strike? Meteor To Hit Earth! A meteor is going to hit Earth! We want to know the probability that it hits land, as opposed to landing in the ocean. • Why would we simulate this? (Why not do an actual experiment?) • What tool could we use to simulate this? • What assumptions are we making? • How will we calculate the probability that a meteor would land on… well, land? Q6. Am I going to die from a lightning strike? Fire Island Assessment Sample of simulation outcomes (km2 lost) Q7. Am I going to die from falling asleep? Results from wearing a heart-rate monitor overnight. X-axis is time (seconds) after going to bed. Y-axis is heart rate in beats per minute. Describe the overall trend. What would happen to Tim (the person monitored) if he kept sleeping? Make an approximate forecast for Tim’s heart-rate after 24hrs asleep. Source: xkcd.com Q8. Is Frane Selak the unluckiest man to ever live? Q9. Are polar bears really stealing our money? Area Bias Example: Polar Bear Population • The World Wildlife Fund (WWF) has written on the threats posed to polar bears by global warming • However, also according to them, about 20 distinct polar bear populations exist accounting for approximately 22,000 polar bears worldwide. • • • • Only 2 of the groups are decreasing 10 populations are stable 2 populations are increasing The status of the remaining 6 populations is unknown • If you are only looking at the 2 groups that are decreasing, it would be easy to say that the “Polar Bear Population is Decreasing”. You need to look at the whole picture to get the whole story