Answer to Question #131389 in Statistics and Probability for moona

Question

in a sample survey 6 estimates were made of the same mean when population mean become known. the following error were computed -35,111,-88,47,-12 and 26. are these errors consists with a hypothesis that population of error has zero mean?

Answer 1

σ ²= Σ(x_i - μ)²/N=3986.472

σ = 63.1

μ=(-35+111-88+47-12+26)/6=8.1666

df=6-1=5, for this value we have t-statistic (x-μ)/(s/$\sqrt n$ )=0.317 and using table P = 0.7640

CI for mean -58.0528 to 74.3860, so we accept that population of error has zero mean