Question

discuss about different methods of decision making with hypothesis testing (p value, critical value and confidence interval) and which one you prefer to use on discussion board

Answer 1

Suppose for a given hypothesis test, the test statistic under H0 is z1 and level of significance is alpha

For simple understanding if we assume test statistic follow normal distribution and test is two sided ,

1.) So, p value = believability of H0 given sample data, that is p value = 2*P(Z>z1). We reject H0 if p value is less than alpha

2.) Critical value is that z0 such that P(|Z| > z1) = alpha. We reject H0 if z1 > z0 or z1 < -z0

3.) We fail to reject H0 if the test statistic that is z1 lies in the confidence interval

We prefer p value approach because if someone gives us new alpha, then we have to calculate z0 and confidence interval again as they are dependent on alpha but we can use p value for any alpha. Moreover, it is easy to interpret. For example if p value is very less, it means very less chance to reject H0