1. Assignment: Solve practice problems WITHOUT looking at the answers.
Apr. 7 Statistic for the day: Average number of handstands an adult male panda does each day: 8
Source: Harper’s index
Assignment:
Solve practice problems WITHOUT
looking at the answers.
These slides were created by Tom Hettmansperger and in some cases modified by David Hunter

2. First, some data: Change is good?
Questions:
1. Do PSU women carry more change than men?
2. Is there a greater proportion of women who carry
change than men?
Data from class, with outlier excluded:
Sample
Size
Proportion carrying change
Mean amount of change
Men 21
5/21 or 23.8%
10.7 cents
Women 34
17/34 or 50.0%
39.7 cents

3. Confidence intervals: Main exam topic
Difference between population values and sample estimates
Rules of sample proportions and sample means
The logic of confidence intervals (what does the confidence coefficient mean?)
SD for proportions, SE for means, and SD for differences between means
How to create CI’s for (a) one proportion; (b) one mean; (c) the difference of two means.
Different levels of confidence

4. Difference between population values and sample estimates
A population value is some number (usually unknowable) associated with a population.
A sample estimate is the corresponding number computed for a sample from that population.
Examples include:
population proportion vs. sample proportion
population mean vs. sample mean
population SD vs. sample SD

5. Rule of sample proportions
IF:
There is a population proportion of interest
We have a random sample from the population
The sample is large enough so that we will see at least five of both possible outcomes
THEN:
If numerous samples of the same size are taken and the sample proportion is computed every time, the resulting histogram will:
be roughly bell-shaped
have mean equal to the true population proportion
have standard deviation estimated by

6. Rule of sample means IF:
The population of measurements of interest is bell-shaped, OR
A large sample (at least 30) is taken.
THEN:
If numerous samples of the same size are taken and the sample mean is computed every time, the resulting histogram will:
be roughly bell-shaped
have mean equal to the true population mean
have standard deviation estimated by

7. The logic of confidence intervals
What does a 95% confidence interval tell us? (What’s the correct way to interpret it?)
IF (hypothetically) we were to repeat the experiment many times, generating many 95% CI’s in the same way, then 95% of these intervals would contain the true population value.
Note: The population value does not move; the hypothetical repeated confidence intervals do.

8. SD for sample proportions
The standard deviation of the sample proportion is estimated by:

9. SE for sample means
The standard deviation of the sample mean is estimated by
This estimate of the SD is called the STANDARD ERROR OF THE MEAN, or sometimes SE mean or SEM.

10. SD for difference between means
The standard deviation of the difference between two sample means is estimated by
(To remember this, think of the Pythagorean theorem.)

11. How to create 95% CI’s for:
A population proportion
A population mean
The difference between two population means
Sample proportion ± 2(SD of sample proportion)
Sample mean ± 2(SE mean)
Diff of sample means ± 2(SD of diff of sample means)

12. Different levels of confidence
A population proportion
A population mean
The difference between two population means
Sample proportion ± 2(SD of sample proportion)
Sample mean ± 2(SE mean)
Diff of sample means ± 2(SD of diff of sample means)
Replace the 2’s with another number from p. 137!

13. Example: 90% confidence interval
Since 90% is in the middle, there is 5% in either end.
So find z for .05 and z for .95.
We get z = ±1.64
90% confidence interval: sample estimate ± 1.64(Std Dev)