Estimation and testing of the population mean when there is only one population (population variance is known)
\[X:32.3,27.0,30.5,36.5,36.2,30.7,30.5,31.0,24.3,27.7\]
head dispersion:
\[\sigma^2=9\]
Point Estimation of Mother Mean
point estimate:
\[\bar{x}=30.67\]
Interval estimation with 95% confidence rate
Interval Estimation:
\[(\bar{x}-1.960\sqrt{\frac{\sigma^2}{n}},\bar{x}+1.960\sqrt{\frac{\sigma^2}{n}})=(28.81,32.53)\]
rejection zone
\[|u_0|≧u(0.05)=1.960\]
test statistic
\[u_0=\frac{\bar{x}-μ_0}{\sqrt{\frac{\sigma_0^2}{n}}}=0.706\]
It cannot be said that the population mean is not μ0=30.
