Consider an hypothetical clinical trial that wishes to employ two statistical (Z
ID: 3363627 • Letter: C
Question
Consider an hypothetical clinical trial that wishes to employ two statistical (Z) tests to assess the hypothesis H_0: =0(=_0) at both an interim point in time and at the completion of the study (where the population standard deviation can be considered known and equivalent for both tests). Call the test statistic from the first interim analysis Z_1 and the test statistic at the completion of the study Z_2. A total of 25 patients were enrolled at the time of the interim analysis, n_1=25 (sample mean outcome = (x_1 ) ), with an additional 11 patients enrolled between the interim analysis and the completion of the study, n_2=11 (sample mean outcome for the n_2 patients= (x_2 ) ). Using the known standard deviation =5/2, write the second test statistic Z_2 as a function of Z_1. [Hint: The Z-stat for any Z-test is Z=((x -_0 ))/(/n)]
Explanation / Answer
A z-test for two means is a hypothesis test that attempts to make a claim about populatiom means.
the main properties of a one sample z-test for two population means are
The z-test can be two tailed test i.e. left tailed or right tailed.
the main principal of hypothesis testing is that the null hpothesis is rejected if the test static obtained is sufficiently unlikely under the assumption that the null hypothesis is true
if the population standard deviation is known then the mean has a normal z distribution..
the z is the z score obtained from normal table. it is the factor of level of confidence which is found by subtracting and adding the maximum error of the estimate from the sample mean.