STAT 3005 Lecture 8: STAT-3005 - Notes - 8-1 - Estimating with Confidence
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Department
Statistics
Course Code
STAT 3005
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H C Tavera

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Daniel T. Eisert STAT-3005
1
8.1 Estimating with Confidence
Chapter VIII: Using Inference
Estimating with
Confidence
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
parameter.
- 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
common.
Confidence Interval Behavior:
- Goal: high confidence with a small margin of error.
- High confidence suggests that the method almost always gives correct
answers.
- A small margin of error suggests that we have pinned down the
parameter precisely.
- 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:
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Description
Daniel T. Eisert STAT-3005 8.1 Estimating with Confidence Chapter VIII: Using Inference Estimating with Recall ~ Statistical Inference provides methods for drawing conclusions about a population from sample data such that: Confidence 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 parameter. - 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 common. Confidence Interval Behavior: - Goal: high confidence with a small margin of error. - High confidence suggests that the method almost always gives correct answers. - A small margin of error suggests that we have pinned down the parameter precisely. - Margin of Error for the Z-Confidence Interval: ( ) - The mrgin 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: = 1
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