What is Statistics?

1
Sampling Distribution for the Sample Proportion
2
Qualitative Responses

• Thus far we have discussed quantitative data
• The survey question we ask has required a
  numerical response
• How far do you live from campus?
• How long did the battery last?
• How much did you spend on health insurance?
• Etc.
• Now we shall ask questions that involve a
  qualitative response
• What is your political party?
• What color is your car?
• Are you a male?

3
Proportions as a Random Variable

• When we isolate one of the possible responses we
  can determine the proportion that gave that
  particular response
• The proportion of Democrats in Orange County
• The proportion of red cars in a parking lot
• The proportion of males at a football game
• If we are going to take a sample of size n Orange
  County voters, then before the sample is taken,
  the proportion of Democrats we will get in the
  survey is a random variable
• If we let X the number of the n respondents
  that say they are Democrats (also a random
  variable since before the sample is taken we do
  not know the value of X), then the proportion of
  Democrats is

4
The Random Variable X

• X the number of successes in n tries
• Binomial but because n large -- can be
  approximated by a normal distribution
• Mean ?X np
• Variance np(1-p)

5
_ THE RANDOM VARIABLE P
Distributed approximately normal with
6
Example

• Suppose 40 of the voters in Orange County are
  Democrats. What is the probability that in a
  sample of 400 randomly selected Orange County
  voters, there will be more than 180 (45)
  Democrats?

7
What is the probability more than 45 of the
sample will be Democrats?
.9795
0 Z
8
Review

• Normal distribution
• Mean ?
• Standard Deviation