Ch9Outline - Statistical Inference The reasoning of...

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Statistical Inference The reasoning of statistical inference rests on asking, "How often would this method give a correct answer if I used it very many times?" If it doesn't make sense to imagine repeatedly producing your data in the same circumstances, statistical inference is not possible. Exploratory data analysis makes sense for any data, but formal inference does not. Inference is most secure when we produce data by random sampling or randomized comparative experiments . Sampling Distributions The purpose of this chapter is to prepare for the study of statistical inference by looking at the probability distribution of some very common statistics: sample proportions and sample means . Example 9.1 - Making Money The mean income of the sample of households contacted by the Current Population Survey was x = $57,045. Example 9.2 – Do you believe in ghosts? The Gallup Poll asked a random sample of 515 U.S. adults whether they believe in ghosts. Of the respondents, 160 said "Yes." 1
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Example 9.3 Baggage Check! Imitation of the population of travelers passing through Guadalajara airport can be done by using a simulation. Customs officers claim that the probability that the light turns green on any press of the button is 0.70. The histogram below shows what would happen if we drew many samples. It approximates the sampling distribution of . p ˆ The distribution of the sample proportion from SRSs of size 100 drawn from a population with population proportion p = 0.7. The histogram shows the results of drawing 1000 SRSs. p ˆ The sampling distribution of a statistic is the distribution of values taken by the statistic in all possible samples of the same size from the same population. Example 9.4 Random Digits The population used to construct the random digits table (Table B) can be described by the probability distribution shown below 2
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Consider the process of taking an SRS of size 2 from this population and computing x for the sample. We could perform a simulation to get a rough picture of the sampling distribution of x . But in this case, we can construct the actual sampling distribution . This figure displays the values of x for all 100 possible samples of two random digits The distribution of x can be summarized by the histogram shown the figure below. Since this graph displays all possible values of x from SRSs of size n = 2 from the population, it is the sampling distribution of x 3
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In Example 9.2 – Do you believe in ghosts? The Gallup Poll asked a random sample of 515 U.S. adults whether they believe in ghosts. Of the respondents, 160 said "Yes." So the proportion of the sample who say they believe in ghosts is 31 . 0 515 160 ˆ = = p The number 0.31 is a statistic . We can use it to estimate the proportion of all U.S. adults who believe in ghosts. This is our
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Ch9Outline - Statistical Inference The reasoning of...

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