b) Repeated tests on the determination of human blood composition during a laboratory analysis are known to be normally distributed. Ten tests on a given sample of blood yielded the values 2.002, 1.958, 2.034, 3.987, 3.987 4.014, 3.009, 1.031, 2.048, 1.024, 1.0886, 1.019, 0.020. Find a 90 per cent confidence interval for true composition of the blood in repeated tests of the sample, and what is the margin of error?
"+3.987+ 4.014+3.009+1.031+2.048"
"+1.024+1.0886+1.019+0.020)=2.094"
"+(2.034-2.094)^2+(3.987-2.094)^2"
"+(3.987-2.094)^2+(4.014-2.094)^2"
"+(3.009-2.094)^2+(1.031-2.094)^2"
"+(2.048-2.094)^2+(1.024-2.094)^2"
"+(0.020-2.094)^2)=1.7055"
"s=\\sqrt{s^2}=1.306"
The critical value for "\\alpha=0.1" and "df=n-1=13-1=12" degrees of freedom is "t_c=z_{1-\\alpha\/2, n-1}=1.782288."
The corresponding confidence interval is computed as shown below:
"=(2.094-1.782\\times \\dfrac{1.306}{\\sqrt{12}}, 2.094+1.782\\times \\dfrac{1.306}{\\sqrt{12}})"
"=(1.448, 2.740)"
Therefore, based on the data provided, the 90% confidence interval for the population mean is "1.448<\\mu<2.740," which indicates that we are 90% confident that the true population mean "\\mu" is contained by the interval "(1.448, 2.740)".
"margin\\ of\\ error=t_c\\times \\dfrac{s}{\\sqrt{n}}"
"=1.782\\times \\dfrac{1.306}{\\sqrt{12}}=0.646"
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