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Statistics: Decisions Through Data

UNIT 20: Confidence Intervals

Summary of the Video

The opening notes that makers of batteries for toys and consumer electronics must estimate the average lifetime in service in order to substantiate advertising claims. The estimate is based on testing a sample of batteries. That's a form of statistical inference .

A simpler example begins the exposition. Will's blood pressure varies over time. His systolic blood pressure readings each day for a week are

125 118 99 133 152 151 132.


This is a sample from the population of Will's varying blood pressure. The mean of the sample is


That's an estimate of the unknown population mean µ. How accurate is this estimate? Would we get very different results from a second sample?

To answer these questions, we need some assumptions. First, our measurements must be far enough apart in time that they don't influence each other—they are independent observations. That's reasonable. Second, as Will's blood pressure varies from day to day, it follows a normal distribution. Experience suggests that's also reasonable. The mean µ of this normal distribution is the parameter we want to estimate. Third, we'll assume we know that the standard deviation of Will's blood pressure distribution is = 20 points. In practice, we would also estimate from data. But we're interested in the reasoning of statistical estimation, and the problem is a bit simpler when is known.

 

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