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).
n = 36, x ̅=105.2, s = 11.2
n = 100, x ̅=105.2, s = 11.2
a.
90%CI=(xˉ−1.645sn, xˉ+1.645sn)90\%CI=(\bar x-1.645\frac{s}{\sqrt{n}},\;\bar x+1.645\frac{s}{\sqrt{n}})90%CI=(xˉ−1.645ns,xˉ+1.645ns)
=(105.2−1.64511.236, 105.2+1.64511.236)=(105.2-1.645\frac{11.2}{\sqrt{36}},\;105.2+1.645\frac{11.2}{\sqrt{36}})=(105.2−1.6453611.2,105.2+1.6453611.2)
=(102.13, 108.27).=(102.13,\;108.27).=(102.13,108.27).
b.
=(105.2−1.64511.2100, 105.2+1.64511.2100)=(105.2-1.645\frac{11.2}{\sqrt{100}},\;105.2+1.645\frac{11.2}{\sqrt{100}})=(105.2−1.64510011.2,105.2+1.64510011.2)
=(103.36, 107.04).=(103.36,\;107.04).=(103.36,107.04).
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