Unit 7-006

# Unit 7-006 - Statistics V3100018.006 UNIT 7 Probability...

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Statistics – V3100018.006 UNIT 7 – Probability Giuseppe Arbia , Catholic University of the Sacred Hearth, Roma, Italy 1

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Statistical inference 2 POPULATION Sample Universal Particular Deduction Induction
3 The problem of statistical inference So far we have considered the case where we only want to describe the data we have in hand. It was as if we had in hand the whole population: no inferential problem.

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4 Let us now consider the case where the individuals that we observe are only a part of a larger population. We ask ourselves How can we exploit the information we have in our sample to estimate the analogous quantities at a population level?
Example 5 POPULATION Sample Universal Particular Deduction Induction x 1 , x 2 ,..., x n ( ) ! m μ Population mean Sample mean

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Example 6 POPULATION Sample Universal Particular Deduction Induction x 1 , x 2 ,..., x n ( ) ! p ! Population Relative frequency Sample Relative frequency
Example 7 POPULATION Sample Universal Particular Deduction Induction x 1 , x 2 ,..., x n ( ) ! s 2 ! 2 Population variance Sample variance

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Back to the deductive exercise sampling distribution of the mean 8
Back to the deductive exercise 9 sampling distribution of the proportion

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Back to our deductive exercise 10 sampling distribution of the median
Back to our deductive exercise 11 sampling distribution of the range

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Back to our deductive exercise 12 True value = 2,92 sampling distribution of the variance
Back to our deductive exercise 13 sampling distribution of the correlation

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