Stat 226 - Lecture 6
01/30/14
Announcements
- Reading quiz due Sunday. Project step 1 due Feb 10th.
- Any questions?
Your Turn
- Finish the heights worksheet, then consider the following:
- For each of the following data scenarios, determine the appropriate measure of center and measure of spread. To answer the question, think about what values are plausible and whether a histogram would yield a more symmetric or a more skewed distribution.
- Household income in the US.
- In-state tuition at US public colleges.
- Heights of people.
- What is the shape of this distribution?
- Why is it that the distribution of heights is bimodal?
- Males tend to be taller than females!
- The solid red line is the population distribution for females.
- In practice, we don't know the population distribution!!! So we have to estimate it using the sample…
- In chapter 12, for simplicity sake, we pretend to know everything about the population distribution.
- Since I'm god, I know the population distribution of heights (solid line).
- Since the distribution is normal, it can be fully described by it's mean and standard deviation:
- The population mean \( \mu \) is 64 inches and standard deviation \( \sigma \) is 1.5 inches.
- The sample mean was 63.98 and the sample standard deviation was 1.55.
- By treating these sample statistics as population parameters, we obtain an estimate of the true probability distribution function (pdf).
- Our estimated pdf is written as:
- \( X \sim N(\mu = 63.98, \sigma = 1.55) \) where \( X \) is a r.v. associated with the height of a female.
- Think about drawing one female at random from the population.
- What is the probability that she is 62 inches or shorter?
- The area under the curve shaded in red!
- We denote this quantity as \( P(X < 62) \)
- We study questions like this in Chapter 12.
- The normal distribution is the most important type of probability distribution function!
- What exactly is a probability distribution function?
