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Confidence interval for population mean using z

Confidence interval for population mean using z -...

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Confidence interval for population mean using  z   Formula where  a  and  b  are the limits of the confidence interval,  is the sample mean,  is the upper (or  positive)  z- value from the standard normal table corresponding to half of the desired alpha level  (because all confidence intervals are two-tailed),   is the population standard deviation, and  σ n  is the  size of the sample.  Example 3 A sample of 12 machine pins has a mean diameter of 1.15 inches, and the population standard  deviation is known to be 0.04. What is a 99 percent confidence interval of diameter width for the 
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Unformatted text preview: population? First, determine the z-value. A 99 percent confidence level is equivalent to p < 0.01. Half of 0.01 is 0.005. The z-value corresponding to an area of 0.005 is 2.58. The interval may now be calculated: The interval is (1.12, 1.18). We have 99 percent confidence that the population mean of pin diameters lies between 1.12 and 1.18 inches. Note that this is not the same as saying that 99 percent of the machine pins have diameters between 1.12 and 1.18 inches, which would be an incorrect conclusion from this test....
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