1. 5.2 Notes

2. Parameter Statistic number that describes a population fixed value
generally unknown
Statistic
number that describes a sample
value can change from sample to sample
used as an estimate for the population parameter

3. EXAMPLE 1:
A polling agency takes a sample of 1500 American citizens and asks them if they are lactose intolerant. 12% say yes. This is interesting, since it has been shown that 15% of the population is lactose intolerant.
12% =
15% =
Population =
Sample =
Parameter of interest =
Statistic
Parameter
All American Citizens
1500 American Citizens
True % of American citizens
that are Lactose Intolerant

4. EXAMPLE 2:
A random sample of 1000 people who signed a card saying they intended to quit smoking were contacted a year after they signed the card. It turned out that 210 (21%) of the sampled individuals had not smoked over the past six months.
21% =
Population =
Sample =
Parameter of interest =
Statistic
All smokers
1000 smokers that signed the card
True % of smokers that
quit smoking

5. Population – All bottles of ketchup produced on Tuesday
EXAMPLE 3:
On Tuesday, the bottles of tomato ketchup filled in a plant were supposed to contain an average of 14 ounces of ketchup. Quality control inspectors sampled 50 bottles at random from the day’s production. These bottles contained an average of 13.8 ounces of ketchup.
14 = =
Parameter
Statistic
Population – All bottles of ketchup produced on Tuesday
Sample – 50 bottles randomly selected
Parameter of interest – True average ounces of ketchup
in Tuesday’s bottles

6. EXAMPLE 4:
An area high school boasts that 85% of all graduating seniors attend college after graduation. A local newspaper polls the next senior class and finds that 74% plan on attending college after graduation.
85% = 74% =
Population:
Sample:
Parameter
Statistic
All students in the next senior class
Students that were polled (unknown number)

7. EXAMPLE 5:
A researcher wants to find out which of two pain relievers works better. He takes 100 people and randomly gives half of them medicine #1 and the other half medicine #2. 17% of people taking medicine 1 report improvement in their pain and 20% of people taking medicine #2 report improvement in their pain.
17% = _________ 20% = __________
Population? Sample? Parameter of interest?

8. Statistic Parameter Measures?
Different Symbols…
Statistic Parameter Measures?
proportion/percent
means/averages

9. p. 223 Read through Example 5.8
Answer the questions.
Pop: All adults; P.I. = % that had bought a lottery ticket
p = 60%
SRS of 100 adults
% that had bought a lottery ticket. 46%
1000 samples
The sample proportions for all 1000 samples
Symmetric, unimodal, centered around .6 and ranges from .44 to .72

10. 8. Sample size is 1523
9. The sample proportions for 1000 samples
10. Symmetric, unimodal, centered around 60, and ranges from 0.56 to 0.64
11. The second has much less spread than the first one.
12. Both are unimodal and symmetric. Also both are centered around 0.60
13.

11. * Different samples give us different results
SAMPLING VARIABILITY
* Different samples give us different results
* Different size samples give us different results
* Bigger samples are better!!
* If we take lots of random samples of the same size, the variation from sample to sample follows a predictable pattern = they make a good graph!
True parameter

12. Larger samples give smaller variability:
* Variability = spread/width of graph
Larger samples give smaller variability:
Lots of samples of size 100
Lots of samples of size 1000
True parameter
True parameter

13. Bias vs Variability Bias is the accuracy of a statistic
Variability is the precision of a statistic

14. Label each as high or low for bias and variability
High Bias
Low Variability
True parameter
True parameter
Low Bias
High Variability

15. Label each as high or low for bias and variability
High Bias
High Variability
True parameter
True parameter
Low Bias
Low Variability

16. Another vocab word… Unbiased Estimator:
- When the center of a sampling distribution (histogram) is equal to the true parameter.
True parameter
True parameter

17. * To reduce bias… use random sampling
* To reduce variability… use larger samples!