A random sample is drawn from a population of known standard deviation 11.3.
Construct a 90% confidence interval for the population mean based on the information
given (not all of the information given need be used).
a. n = 36, š„Ģ = 105.2, š = 11.2
b. n = 100, š„Ģ = 105.2, š = 11.2
a.
The critical value forĀ "\\alpha = 0.1"Ā isĀ "z_c = z_{1-\\alpha\/2} = 1.6449."
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}})"
"=(105.2-1.6449\\times\\dfrac{11.3}{\\sqrt{36}}, 105.2+1.6449\\times\\dfrac{11.3}{\\sqrt{36}})"
"=(102.1021, 108.2979)"
Therefore, based on the data provided, theĀ 90%Ā confidence interval for the population mean isĀ "102.1021 < \\mu < 108.2979," which indicates that we areĀ 90%Ā confident that the true population meanĀ "\\mu" is contained by the intervalĀ "(102.1021, 108.2979)."
b.
The critical value forĀ "\\alpha = 0.1"Ā isĀ "z_c = z_{1-\\alpha\/2} = 1.6449."
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}})"
"=(105.2-1.6449\\times\\dfrac{11.3}{\\sqrt{100}}, 105.2+1.6449\\times\\dfrac{11.3}{\\sqrt{100}})"
"=(103.3413, 107.0587)"
Therefore, based on the data provided, theĀ 90%Ā confidence interval for the population mean isĀ "103.3413 < \\mu < 107.0587," which indicates that we areĀ 90%Ā confident that the true population meanĀ "\\mu" is contained by the intervalĀ "(103.3413, 107.0587)."
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