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February 7 2012 – Week 5

TG. SP.

- Today we will talk about confidence interval

10 things you should know about C.I.

1. Confidence intervals are all about range of possible values of a parameter

expressed

Whether or not if it is high or not, it is not based on entire population.

It is sample-based. What if it’s wrong?

The quality of sample you have is essential

It is based on theoretical idea of the sample

If you can just come back to visualizing the concrete it will provide the

estimate of the population

You have to translate it into a theoretical sample distribution. What is

the possibility that you got Gwen Stefani? Very unlikely.

2. CIs are based on the notion that we use sample stats to estimate the value of

a population parameter

Not a distribution of scores on the first test

The sample size matters and that is why sample size has influence on

error

3. Calculation for a CI is as follows (refer to the slide)

Instead of memorizing formula the calculation is point estimate

The size of error is essential

How far am I off from the point?

To calculate the error term you need standard deviation.

The sample is really critical in this

Correlation between education and income is related. It doesn’t make

sense to you now, it will later on after the first test.

4. Obtain the standard error

Go back to the idea of spread was small, like 7,8,7,8,7,8, it is very little

spread. However, if it is 2,7,4,0,8, sample deviation is huge so more

standard error

Taking what you have and comparing to hypothetical

5. We need to obtain the error term

6. What is the critical Z score and how to obtain it

1.96 is the number you should remember

Low probability of scooping up a sample

The larger the standard error, the questionable the answer.

What is the true population mean

o The standard error size is an indicator of how many

variability is there in population

7. What happens to the size of width of the CI when the size of sample standard

deviation increases?

Sample-to-sample estimates may be worse

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