Statistical Help

Question

Assume that the significance level is a = 0.05.  Use the given information to find the P-value and the critical value with

H₁ ; P ≠1/2, the test statistic is z = -1.36

 

p-value = ____

 

the critical value is/are = ______

Answer 1

First, this is a two-sided test. We know this because the alternate hypothesis is =/= rather than a single direction. This means we are looking for evidence on either side of 1/2 (or on either side of a z-score of 0). For a 5% alpha, this means our critical value (z-score) is that which retains the MIDDLE 95% (excluding a total of 5% on the extremes, evenly distributed). Think back to the Empirical Rule from earlier in the year....that's approximately a z-score of 2....or more precisely now that you're at this point in the curriculum: 1.96. Since we are looking for evidence both above and below, it will be +/- 1.96. Since our z-score is much closer to 0 than -1.96 we know our p-value is going to be much higher than 5% and we will fail to reject Ho....so really there is no point in finding a p-value. But indulging the question, using a calculator or z-table, find the area of a normal curve BELOW a z-score of -1.36: 0.087. But we aren't done! Because this is 2-sided we need to double the p-value to account for the same area above positive 1.36! 0.087x2 = 0.174. That's our final p-value. Again, well above alpha = 0.05. I hope this helps!