A statistics practitioner took a random sample of 50 observations from a population with a standard deviation of 25 and sample mean of 100. The 95% confidence interval of population mean is
The critical value for "\\alpha = 0.05" is "z_c = z_{1-\\alpha\/2} = 1.96."
The corresponding confidence interval is computed as shown below:
"=(100-1.96\\times\\dfrac{25}{\\sqrt{50}}, 100+1.96\\times\\dfrac{25}{\\sqrt{50}})"
"=(93.07, 106.93)"
Therefore, based on the data provided, the 95% confidence interval for the population mean is "93.07 < \\mu < 106.93," which indicates that we are 95 %confident that the true population mean "\\mu" is contained by the interval "(93.07, 106.93)."
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