Daniel T. Eisert STAT-3005
Recall ~ Statistical Inference provides methods for drawing conclusions
about a population from sample data such that:
1. Collect data from a representative sample of a given population.
2. Make an inference about the population.
Confidence Level: the overall capture rate if the method is used multiple
times. The confidence level can be thought of the success rate for the method.
- The sample mean will vary from sample to sample.
- When using the method , of these
intervals capture the unknown population mean .
- Interpretation: 95% of all possible samples of a given size from this
population will result in an interval that captures the unknown
- The sampling distribution of tells us how close to the sample mean
is likely to be.
- Typically chose confidence levels higher than 90%; 95% is the most
Confidence Interval Behavior:
- Goal: high confidence with a small margin of error.
- High confidence suggests that the method almost always gives correct
- A small margin of error suggests that we have pinned down the
- Margin of Error for the Z-Confidence Interval:
- The margin of error decreases when:
1. gets smaller.
2. The confidence level decreases.
3. gets smaller.
4. gets smaller. Since is square rooted, we must take four times as
many observations to cut the margin of error in half.
Spread & Sample Size:
- The spread in the sampling distribution of the mean is a function of the
number of individuals per sample.
- The larger the sample size, the smaller the standard deviation (spread)
of the sample mean distribution.
- The spread decreases at a rate equal to .
Choosing the Sample Size (Proportion):
- When planning a study, chose a sample size that allows one to estimate
a population proportion within a given margin of error: