Answer to Question #264174 in Statistics and Probability for Myra

Question #264174

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



1
Expert's answer
2021-11-11T13:13:25-0500

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:


"CI=(\\bar{X}-z_c\\times\\dfrac{\\sigma}{\\sqrt{n}}, \\bar{X}+z_c\\times\\dfrac{\\sigma}{\\sqrt{n}})"

"=(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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