3_3_Handout - 3.3 Toward Statistical Inference Statistical...

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3.3 Toward Statistical Inference Statistical inference is using a fact about a sample to estimate the truth about the whole population. A simple random sample (SRS) of size n consists of n individuals from the population chosen in such a way that every set of n individuals has an equal chance to be the sample actually selected. A parameter is a number that describes the population. A parameter is a fixed number, but in practice we do not know its value. A statistic is a number that describes a sample. The value of a statistic is known when we have taken a sample, but it can change from sample to sample. We often use a statistic to estimate an unknown parameter. EX) A researcher takes a nationwide SRS of 2500 adults that asks if they agree with the statement “I like to shop.” Suppose 1650 agreed. p ˆ = (1650/2500) = 0.66 = 66% p ˆ = 0.66 is a statistic (proportion of sample that agrees) p = ? is a parameter (proportion of population (all US adults) that would agree if asked) If the researcher sampled another 2500 adults, he would almost certainly get a different value for p ˆ . Sampling variability means that the value of a statistic varies in repeated random sampling. if the variation when we take repeat samples from the same population is too great, we can’t trust the results of any one sample advantages of random samples •choosing at random eliminates bias •if we take lots of random samples of the same size from the same population, the variation from sample to sample will follow a predictable pattern What would happen if we took many samples? •take a large number of samples from the same population. •calculate the sample proportion p ˆ for each sample. •make a histogram of the values of p ˆ •examine the distribution displayed in the histogram (shape, center, and spread)
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too expensive to take many samples to create histogram- can do simulation suppose you knew
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3_3_Handout - 3.3 Toward Statistical Inference Statistical...

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