1. Target for Today Know what can go wrong with a survey and simulation
Know difference between a statistic and a parameter
Write down the five steps for setting up a simulation
Can make a sampling distribution
Can determine confidence interval

2. Notes: Survey What can go wrong with a Survey?
Volunteers: bias since only selected group voluntarily responds
Convenience: who is easy to talk to does not always represent the whole population (people in prison, homeless)
Sample Frame: frame may not include all important groups (if choose people from phone book lots not listed)
Undercoverage: some groups not equally represented
Non respondents: people who do not respond may represent an important group

3. Notes: Simulation What can go wrong with a Simulation?
The simulation only tells you what might happen not what does happen
You do not select the right numbers to reflect the outcome
You do not run enough trials

4. What is the difference between a parameter and a statistic?

5. p.270 Statistic – is a numerical value computed from a sample.
Parameter – is a numerical value associated with a population.
Essentially, we would like to know the parameter. But in most cases it is hard to know the parameter since the population is too large. So we have to estimate the parameter by some proper statistics computed from the sample.

6. A closer look at some statistics

7. Sampling Distribution
1. Choose sample size n
Run trials and find 𝑝 for each trail
3. Summarize results:
a) Histogram for all 𝑝
b) Mean = 𝑝 # 𝑜𝑓 𝑡𝑟𝑖𝑎𝑙𝑠
c) Stdev =

8. The survey asks 200 random under-age students.
A survey is undertaken to determine the proportion of PSU students who engage in under-age drinking.
The survey asks 200 random under-age students.
Suppose the true population proportion is 60% or p=.6

9. The proportion of under-age
students who drink

10. A point estimate. Find by averaging all trials.
Sample proportion
(a statistic)
A point estimate. Find by averaging all trials.
𝑝 = population proportion + random variation
Standard deviation (use p if can otherwise 𝑝 ) or
Problem with point estimate is it gives no information of how close the value is to the unknown population parameter

11. What are the steps for finding the Sampling Distribution for the PSU study?

12. Step #1: determine the sample size n
Will 200 students be enough
if the true proportion of students who drink is .6?
#1: choose n
Sample Size condition
Need condition met to use the normal curve
np > and n(1-p)> 10
Where
n = number in each trial
P = population proportion

13. Step #2: Repeated Trials
If we do this survey over and over and make a histogram of , what would the histogram look like?
Sample (n=200)
Sample Proportion 1 2 3 4 5 …
150,000
Imagine repeating this survey many times, and each time we record the sample proportion of those who have engaged in under-age drinking.

14. Summarize results with histogram
53%
67%
60%

15. How confident are you about
But is p-hat enough
information???
How confident are you about
this statistic?

16. P-hat: point estimate
A single number.
No info on how accuracy of your statistic
interval estimate
Gives info on how close the statistic is to the real thing
We are 68% confident that between 67% and 53% of PSU student drink underage
Problem with point estimate is it gives no information of how close the value is to the unknown population parameter
53%
67%
Upper
Confidence
Limit
Lower
Confidence
Limit
Point Estimate

17. Step #3: build confidence interval
(CI)
99%: z = 2.58
95%: z = 1.96
90%: z = 1.64
The probability that the true population falls between two sets of values:
lower confident limit:
upper confident limit:
Margin of Error
Point Estimate
Lower
Confidence
Limit
Upper