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Recipient email: 16Essential medical statistics2233For example, if one makes the parametric assumption that the underlying distribution is a normal distribution, and has a sample set {X1,.,Xn}, then confidence intervals and credible intervals may be used to estimate the population mean and population standard deviation of the underlying population, while prediction intervals may be used to estimate the value of the next sample variable, Xn+1doi:10.1002/for.3980140502{displaystyle N(0,sigma ^{2}).} Taking the ratio of the future observation and the sample standard deviation cancels the , yielding a Student's t-distribution with n1 degrees of freedom:where Ta is the 100(1p/2)th percentile of Student's t-distribution with n1 degrees of freedomUnknown mean, known variance[edit]p.472

Contrast with other intervals[edit]{displaystyle {frac {X{n+1}-{overline {X}}{n}}{s{n}{sqrt {1+1/n}}}}sim T^{n-1}.} Prediction interval z 75% 1.15[3] 90% 1.64[3] 95% 1.96[3] 99% 2.58[3] This approach is usable, but the resulting interval will not have the repeated sampling interpretation[4] it is not a predictive confidence intervalS v = [ v x 0 0 0 v y 0 0 0 v z ] 4611which would be equivalent to d0c5882bee

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