Estimate a population total from a simple random sample

The total is the mean scaled by N, so its variance is scaled by N^2; the coefficient of variation, identical for the two, is returned to make that visible.

Usage

Srstotal(y, N, level = 0.95)

Arguments

y

Sample observations.

N

Population size.

level

Confidence level.

Value

List with estimate, se, ci_lower, ci_upper, mean, cv, fpc, N, n.

Details

Formula: Yhat = N ybar; v(Yhat) = N^2 (1 - f) s^2 / n, f = n/N

References

Cochran (1977), Sampling Techniques, 3rd edition, Chapter 2: Yhat = N ybar with V(Yhat) = N^2 (N - n)/N S^2/n for simple random sampling without replacement. Cross-checked against the CRAN package samplingbook 1.2.4, whose Smean uses the same finite-population- corrected variance for the mean.

Examples

b <- c(1.5, 2.5, 3.5)
res <- Srstotal(y = b, N = 3L)
res
#> $estimate
#> [1] 7.5
#> 
#> $se
#> [1] 0
#> 
#> $ci_lower
#> [1] 7.5
#> 
#> $ci_upper
#> [1] 7.5
#> 
#> $mean
#> [1] 2.5
#> 
#> $cv
#> [1] 0
#> 
#> $fpc
#> [1] 0
#> 
#> $N
#> [1] 3
#> 
#> $n
#> [1] 3
#> 
#> $method
#> [1] "SRS population total, Yhat = N ybar"
#> 
#> attr(,"class")
#> [1] "morie_rich_result" "list"