WEBVTT

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Here is the problem: A sample of 64 has mean 50; the population standard deviation is 8. Find the 90 percent confidence interval for the mean.

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Build a 90 percent confidence interval for the population mean μ.

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Standard error of the mean.

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Critical value for 90 percent confidence. The middle 90 percent leaves 5 percent in each tail. σ is treated as known, so the standard normal distribution gives the critical value.

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Margin of error.

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Interval: estimate plus or minus margin.

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So the answer is 90 percent CI: (48.3551, 51.6449); margin of error 1.64485.

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We are 90 percent confident that the population mean μ lies between 48.3551 and 51.6449. The confidence describes the method: about 90 percent of intervals built this way from repeated samples would capture the true value.

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The interval is centred on the estimate: (48.3551 plus 51.6449) / 2 equals 50.