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Stats 309 12-3

# Stats 309 12-3 - 12.3 Inference on Population Proportion We...

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12.3 Inference on Population Proportion We use proportions when we have qualitative data. If we have qualitative data, all we can do is count the number of occurrences of each value. From the counts we calculate proportions. For example, if we ask consumers of a particular product which brand they prefer (A, B, C or D), numbers are arbitrary: can’t calculate mean or variance. So, maybe the manufacturers of brand A want to know something about the proportion of the pop who prefer their brand. In that case, we count how many people chose brand A out of how many people we asked. The people who chose brand A are labeled ‘successes’ and all others are ‘failures’. The logical statistic to use to estimate and test the population proportion would be the sample proportion.

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So, we take a sample and calculate the sample proportion . ˆ x p n = The sampling distribution of p-hat is approximately normal if our n is large enough, so we can use the Z table. To check to see if our n is large enough,
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Stats 309 12-3 - 12.3 Inference on Population Proportion We...

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