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We use estimated values for each uncertain parameter, and estimated errors typically chosen as half of an interval estimate of the parameter.
Knowledge of the sampling distribution is necessary for the construction of an interval estimate for a population parameter.
In the large-sample case, a 95% confidence interval estimate for the population mean is given by x̄ ± 1.96σ/√n.
This is why a probability sample is needed; without a probability sample, the sampling distribution cannot be determined and an interval estimate of a parameter cannot be constructed.
Owing to the presence of the n1/2 term in the formula for an interval estimate, the sample size affects the margin of error.
The sampling distribution of x̄1 − x̄2 would provide the basis for a confidence interval estimate of the difference between the two population means.
With knowledge of the sampling distribution of the sample proportion, an interval estimate of a population proportion is obtained in much the same fashion as for a population mean.
It should be noted from the formula for an interval estimate that a 90% confidence interval is narrower than a 95% confidence interval and as such has a slightly smaller confidence of including the population mean.
In the small-sample case i.e., where the sample size n is less than 30 the t distribution is used when specifying the margin of error and constructing a confidence interval estimate.
b Interval estimate.
b Interval estimate and theoretical value.
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