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11.959 < 19... so we accept!

so we can use our reduced model.

Therefore our estimate is , the mean!If you want to learn more check out When did the Spain become the first European superpower?

→ Start of Chapter 12

 If you want to learn more check out What are the six weather variables?

{ Designing Experiment to increase Accuracy We also discuss several other topics like chu yuan chang

→ Why do we want to do this?

• minimize the experiment costs
• obtain better results 

We also discuss several other topics like What term refers to areas of personal freedom constitutionally protected from government power?
If you want to learn more check out What are the roles of the sensory nerves and blood vessels?

→ Consider the problem of estimating the difference between a pair of populations,  If the total sample size is , then how many observations should the experimentar select from the populations 1 and 2? We also discuss several other topics like Sleep deprivation can cause?

Recall: (in ch.8 and 10):

        We estimate  with with the standard error

Note:                 

We want a smaller standard error , since it implies better estimation results.

In addition, if we assume

We will prove in this case, is minimized.

Proof: let b denote the fraction of the total n observations assigned to the sample from population 1.

                

        

ie. is minimized when

                

{ The Matched - Pair Experiment

→ Paired Data : In many experiments, the samples are paired rather than independent. A commonly occurring situation is one where repeated observations are made on the same sampling unit.

ex. Weighing the same person beforeand after he or she participates in a

weight loss program.

→ Advantage of using paired data:

Comparing two populations on the paired data can be a very effective experimental

design that can control for extraneous sources of variability and result in decreasing the

standard error of

Why??

→ let

                

                → you know they are correlated for paired data

        ← Thus, we look at cor also.

        p: a common correlation coefficient

Define                         

                                (for different people, they are independent)

                                The differences in  for each person.

        

A natural estimator for  is

        

References: