Sampling Variability

1
Sampling Variability

• Section 8.1

2
Sampling Distribution

• Represents the long run behavior of the mean when
  sample after sample is selected.
• It is used to find out more about a parameter of
  a population.

3
Parameter

• Quantity computed from values in a population
• Usually not known

4
Statistic

• Quantity computed from values in a sample.
• Computed directly from sample data

5
Identify the population, parameter, sample and
statistic.

• The Gallup Poll asked a random sample of 515 U.S.
  adults whether or not they believe in ghosts. Of
  the respondents, 160 said yes.

6
Identify the population, parameter, sample and
statistic.

• On Tuesday, the bottles of Arizona Iced Tea
  filled in a plant were supposed to contain an
  average of 20 ounces of iced tea. Quality
  control inspectors sampled 50 bottles at random
  from the days production. These bottles
  contained an average of 19.6 ounces of iced tea.

7
Identify the population, parameter, sample and
statistic.

• On a New York-to-Denver flight, 8 of the 125
  passengers were selected for random security
  screening before boarding. According to the
  Transportation Security Administration, 10 of
  passengers at this airport are chosen for random
  screening.

8
Sampling Variability

• The observed value of a statistic will depend on
  the sample selected.
• In other words it will vary from sample to
  sample.

9
Sampling Distribution

• Distribution of the values of a statistic
• Notice what the relationship is between the mean
  of the population the sample.

10
Abby -24Bill 25Cindy- 26Dave 27Ed 28
Find the sampling distribution if we look at
samples of size 2. (sample with replacement do
all combinations!)
11
2, 4, 6, 8 Size 2 samples - mean
12
2, 4, 6, 12 Size 2 samples - range
13
Unbiased Estimator

• If the mean of the sampling distribution is equal
  to the true value of the parameter being
  estimated.

14
Homework

• Page 428 (1-19)odd, (21-24)