Question

Find the best critical region for the hypothesis that a coin is well constructed for a random sample. of 64 launches taking a significance level of 0.05. Repeat the same with a significance level of 0.01.

Answer 1

hypothesis proportion,   po=    0.5                      
significance level,   α =    0.050                      
sample size,   n =   64                      
                              
std error of sampling distribution,   σpo = √(po*(1-po)/n) = √ (   0.500   *   0.500   /   64   ) =   0.0625

Zα/2   = ±   1.960   (two tailed test)                  

these Z-critical value corresponds to some X critical values ( X critical), such that                              
-1.960 ≥(p^ - po)/σpo≥ 1.960                      
-1.960   *σpo + po≥ p^ ≥ 1.960   *σpo + po                  
0.3775 ≥ p^ ≥ 0.6225                      

===============

α=0.01

Zα/2    = ± 2.576 (two tailed test)                    

these Z-critical value corresponds to some X critical values ( X critical), such that                                
-2.576 ≥(p^ - po)/σpo≥ 2.576
-2.576 *σpo + po≥ p^ ≥ 2.576 *σpo + po                    
0.3390 ≥ p^ 0.6610