Question

Consider a significance test for a null hypothesis versus a two-sided alternative. Give a value of z (±0.001) that will give a result significant at the 4 % level but not at the 2 % level.

Answer 1

Consider a significance test for a null hypothesis versus a two-sided alternative. Give a value of z (±0.001) that will give a result significant at the 4 % level but not at the 2 % level. We use standard normal table to solve this.

The value of z at 4% level of significance is when alternative is two sided

z_0.04/2 = z_0.02 = -2.053

z is symmetric in nature, so, z_0.98 = 2.053

The value of z at 2% level of significance is when alternative is two sided

z_0.02/2 = z_0.01 = -2.326

z is symmetric in nature, so, z_0.99 = 2.326

So, z-value is in the interval -2.326<z<-2.053 or 2.053<z<2.326, it will be significant at 4% level but not at the 2% level.