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Testing Statistical Hypotheses

In the previous chapter, we found that by computing a confidence interval, we could obtain a range of likely values for the population parameter we're estimating. Not only that, but we could do a heuristic ``test'' to see if claims were correct by seeing if the confidence interval captured the claimed value. For example, a manufacturer claims that the average lifetime of an electronic component is 32 hours. We could take a sample of electronic components of size n and measure their lifetime. By measuring the sample mean and variance, we can compute a 95% confidence interval. If 32 fell within our interval, we said we would believe the claim of the manufacturer. If it didn't fall within the interval, we wouldn't believe the claim. Hypothesis testing/ is a formal way of testing claims such as these and is closely related to confidence intervals.



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