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A simple random sample of 60 items from a population with σ = 9 resulted in a sample mean of 31. If required, round your answers to two decimal places.
a. Provide a 90% confidence interval for the population mean.
b. Provide a 95% confidence interval for the population mean.
c. Provide a 99% confidence interval for the population mean.

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Blitztiger
The confidence interval is defined by: [tex](x - z* \frac{\sigma}{\sqrt{n}}, x + z* \frac{\sigma}{\sqrt{n}})[/tex]
[tex](31 - z* \frac{9}{\sqrt{60}}, 31 + z* \frac{9}{\sqrt{60}})[/tex]
a. For a 90% confidence interval, z = 1.64. Then the confidence interval is: [tex](31 - 1.64* \frac{9}{\sqrt{60}}, 31 + 1.64* \frac{9}{\sqrt{60}}) = (29.0945, 32.9055)[/tex]
b. For a 95% confidence interval, z = 1.96. The CI is: [tex](31 - 1.96* \frac{9}{\sqrt{60}}, 31 + 1.96* \frac{9}{\sqrt{60}}) = (28.7227, 33.2773)[/tex]
c. For a 99% confidence interval, z = 2.57. The CI is: [tex](31 - 2.57* \frac{9}{\sqrt{60}}, 31 + 2.57* \frac{9}{\sqrt{60}}) = (28.0139, 33.9861)[/tex]

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