Suppose we observe X∼Binomial(n,p)X \sim \text{Binomial}(n, p)X∼Binomial(n,p). What is the Score test statistic for H0:p=p0H_0: p = p_0H0:p=p0?
Z=Xˉ−p0p0(1−p0)/nZ = \frac{\bar{X} - p_0}{\sqrt{p_0(1-p_0)/n}}Z=p0(1−p0)/nXˉ−p0
Z=Xˉ−p0Xˉ(1−Xˉ)/nZ = \frac{\bar{X} - p_0}{\sqrt{\bar{X}(1-\bar{X})/n}}Z=Xˉ(1−Xˉ)/nXˉ−p0
The statistic relies on the variance under H0H_0H0
The statistic relies on the sample variance