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Topic 9: Confidence Interval, But the is a cost of having greater…
Topic 9: Confidence Interval
CLT (Central Limit Theorem)
provides the theoretical
foundation
of statistical inference
Point & Interval Estimate
i) Estimation
We do not have exact answers yet we could estimate.
And it is usually the value of the population we are estimating.
Point Estimation
Interval Estimation
More complicated but safer
Cuz by guessing a range of values, we are more likely to include the population values.
Confidence Interval
A range of values that is likely to contain the true value of the populate parameter
Associated with **degree of
confidence** (used α to describe a probability that corresponds to an area.)
First Step in Interval Estimate
Exact value of alpha depends on the nature of the research situation, but a 0.05 probability is commonly used
Alpha Value
When alpha = 0.05, the confidence level = 95%
Meaning that over the long run, the researcher is willing to be
Wrong
only 5% of the time....
How do we interpret a 95% confidence interval?
Interpretation 1
2 important features
of this def:
i) NOT every interval constructed includes the parameter.
ii) If we construct 100 intervals and use the 95% level, NOT exactly 95 of the intervals would include the parameter
A 95% confidence interval means that ABOUT 95% of the similarly constructed interval contain the parameter being estimated
Interpretation 2
A 95% confidence interval means that 95% of the sample mean (for a specified sample size) lies within 1.96 std deviation of the hypothesized population mean
99% (It means 99% of sample means lie within 2.58 std deviation of hypothesized population mean)
Why not we have 100% Confidence
Nothing comes for free in this world
The greater the confidence level, the greater the probability that the interval would include µ.
Becuz the greater the confidence, the wider the interval, hence less precise the estimate.
There is always a trade off
Selecting a simple size
3 factors
that determine size of sample
Maximum error allowed (Tolerate)
Variation in the population
Degree of conficence
But the is a cost of having greater confidence, WHY?