Review Lecture

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Review Lecture

• Preparing for the midterm

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Statistics on midterm

• Let Ymidterm average of first three
  assignments
• For spring 2004, interpret the following

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To increase Y

• Know all the material
• Dont be surprised
• Be fast
• Recognize different types of problem
• Find formulas quickly, calculate quickly
• Write up briefly
• Finish the Practice Midterm
• in 90 minutes
• Note. Topics not on Practice Midterm are fair
  game
• e.g., sampling and sampling variation

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Other ways to study

• Go over old homework
• making sure you can correct your mistakes
• Go over lecture notes
• Do examples before you see my solution
• Do odd numbered chapter problems
• Check your answers in the back of the book
• Remember the book doesnt use t in confidence
  intervals for meansbut you do!

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Allowed materials

• Formula sheet you can annotate with
• interpretations
• examples
• mistakes youve made in the past
• Tables you can annotate
• Calculator
• Pencil (recommended) or pen

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First half of course
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Data sets and frequency tables

• Distinguish a frequency table from a data set
• Turn a data set into a frequency table
• and vice versa
• Calculate and interpret
• (cumulative) frequencies
• (cumulative) proportions/percentages

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Graphics

• Turn a frequency table into a
• histogram
• bar chart
• pie chart
• Use vocabulary to describe and explain shape
• left/right skew, symmetry, (uni/bi/multi)modal
• Distort graphics
• Recognize and correct others distortions

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Measures of center

• Calculate each measure of center
• from a data set
• from a frequency table
• Interpret each measure of center
• Use the measure in a sentence that shows a naïve
  reader what it means
• Know which statistics are sensitive and robust
• Anticipate the effects of adding/removing extreme
  values

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Measures of variation

• Calculate each measure of variation
• from a data set
• from a frequency table
• Interpret each measure of variation
• Use the measure in a sentence that shows a naïve
  reader what it means
• Know which statistics are sensitive and robust
• Anticipate the effects of adding/removing extreme
  values

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Sampling

• Identify the population being sampled
• Is it the right population?
• If not, how might the right population differ?
• Know how to take a simple random sample
• and whats wrong with alternatives
• Recognize sampling variation when you see it
• Calculate and interpret the standard error (
  margin of error)
• What decreases/increases the standard error?
• How sure can you be that the sample mean will be
  within X standard errors of the population mean?

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Confidence intervals for the mean

• Calculate a confidence interval for the mean
• Interpret it
• Whats being estimated?
• Why are we uncertain?
• Whats certain / whats uncertain?
• What does it mean to be 95 confident?
• Is it small enough to be informative?
• How can we make it smaller?
• Is it smaller than it needs to be?
• How can we make it bigger?

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Sampling for proportions

• Identify the population being sampled
• Is it the right population?
• If not, how might the right population differ?
• Recognize sampling variation when you see it
• http//www.ohiotreasurer.org/images/f-stat3w.jpg
• Calculate and interpret the standard error (
  margin of error)
• What decreases/increases the standard error?
• How sure can you be that the sample proportion
  will be within X standard errors of the
  population proportion?

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Confidence interval for a proportion

• Calculate a confidence interval for a proportion
• Interpret it (use percentage language)
• Whats being estimated?
• Why are we uncertain?
• Whats certain / whats uncertain?
• What does it mean to be 95 confident?
• Is it small enough to be informative?
• How can we make it smaller?
• Is it smaller than it needs to be?
• How can we make it bigger?

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Means vs. proportions

• Calculate confidence intervals
• for means, using t
• for proportions using Z
• different standard errors formulas
• How to tell a proportions problem from a means
  problem
• Bottom line A proportions problem involves a
  dummy variable
• keywords
• means problem may say mean or average and give a
  standard deviation
• proportions problem may say percentage or
  probability or chance
• keywords not 100 reliable
• see slide 2

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Bonus slides
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Turn this into a frequency table
What of players are at most 80 inches
tall? What are at least 80 inches tall?
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Calculate and interpret measures of center from
the raw data set
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Calculate and interpret measures of center from
the frequency table
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Calculate and interpret measures of variation
from the raw data set
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Calculate and interpret measures of variation
from the frequency table
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Calculate a confidence interval for a mean

• Suppose those players were a sample of the NBA
• Whats a point estimate for the mean height in
  the NBA?
• Whats a 95 confidence interval?
• Use t

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Calculate a confidence interval for a proportion

• Whats a point estimate for the of NBA players
  who are at least 80 inches tall?
• Whats a 99 confidence interval?
• Use Z