# Chapter 6 Confidence Interval Estimates

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Estimation
the process of determining a likely value for a population parameter.
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Point estimate
for a population parameter is a single-valued estimate of that parameter; the population mean or proportion.
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Confidence interval
estimate; a range of values that are likely to cover the true population parameter with a level of confidence attached, such as 95% confidence that the interval contains the unknown parameter.
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Point estimate +/- margin of error
the general form of confidence interval.
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Two types of estimates that can be produced for any population parameter.
Point estimate and confidence interval.
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For estimation, classifying the key study variable (outcome or endpoint) ...
Dichotomous or continuous.
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The number of comparison groups in the investigation...
dictate the appropriate estimation technique.
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Usual confidence intervals chosen.
90%, 95%, and 99%. Although any level can be chosen between 0 & 100%.
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What is determined first when calculating the confidence interval?
Point estimate
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What does it mean when we choose a confidence level of 95%?
There is a 95% probability that a confidence interval will contain the true population mean.
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Confidence Interval Formula for a continuous outcome.
(for 95% confidence level) X +/- (z)1.96 σ/√n
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Margin of error formula
(for 95% confidence level) 1.96 σ/√n
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The higher the confidence level, the larger the
z values - which translate to larger margins of error and wider confidence intervals.
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To be 99% confident that a confidence interval contains the true unknown parameter, we need
a wider interval.
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t values for confidence intervals are larger for
smaller samples, resulting in larger margins of error. There is more imprecision with small samples.
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What does it mean when we take an estimate of a population using a 95% confidence level with a sample of 100 people?
95 out of 100 confidence intervals will contain the true mean value μ, and 5 out of 100 will not include the true mean value.
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Sample standard deviation sign
s
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Statement when confidence interval is made for continuous outcome.
We are 90%, 95%, 99% confident that the true mean in the population is between a and b.
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Confidence interval formula for a dichotomous outcome.
p̂ +/- z√p̂1 (1-p̂)/n
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Standard error
SE(p̂) = √p̂1 (1-p̂)/n
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Statement when confidence interval is made for dichotomous outcome.
We are 90%, 95%, 99% confident that the true proportion is between a and b.
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What is the middle of the interval?
The sample mean
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The size of the confidence interval is determined by three (3) things:
1. how confident you want to be in the estimate, 2. standard deviation in the underlying population, 3. the size of the sample
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The more confident or the higher your confidence level