Question

.In a sample survey ,six estimates were made of the same mean.When the population mean became known ,the following errors were computed:-45,112,-89,-47,-13,26.Are these errors consistent with the hypothesis that the population of errors has a zero mean?Assume that the errors are normally distributed. *

Answer 1

$\overline{X}=(-45+112-89-47-13+26)/6=-9.33$

$s=\sqrt{\frac{n(\sum X^2)-(\sum X)^2}{n(n-1)}}=\sqrt{\frac{6*25544-(-56)^2}{6*5}}=\sqrt{\frac{150128}{30}}=70.74$

d.f. = n-1 = 6-1 = 5

We need to use t-test. Let's use $\alpha=0.05$:

1) H₀: $\mu=0$, H₁: $\mu\ne0$

2) critical t values (two-tailed, $\alpha=0.05$, d.f. = 5) = ±2.57

3) t(test value)=$\frac{\overline{X}-\mu}{s/\sqrt{n}}=\frac{-9.33-0}{70.74/\sqrt{6}}=-0.32$

4) Do not reject the null hypothesis since -2.57<-0.32<2.57.

5) These errors are consistent with the hypothesis that the population of errors has a zero mean.