Question

You are conducting a quality control test for bolts delivered by your supplier. The diameter of the bolt must be within 0.01 mm. of the size of pre-drilled holes in shaped metal parts for the machine that your company manufactures. Suppose that the true proportion of bolts that meet your specs is p = 0.82. What is the minimum sample size required for the sample proportion to have approximately a Normal distribution?

Round your answer to the nearest integer. (Note: in practice, you should round up. However, except for small minimum sample sizes, the two methods of rounding have about the same effect on the results.)

Answer 1

sample proportion ,   p̂ =    0.82                          
sampling error ,    E =   0.01                          
Confidence Level ,   CL=   0.95                          
                                  
alpha =   1-CL =   0.05                          
Z value =    Zα/2 =    1.960   [excel formula =normsinv(α/2)]                      
                                  
Sample Size,n = (Z / E)² * p̂ * (1-p̂) = (   1.960   /   0.01   ) ² *   0.82   * ( 1 -   0.82   ) =    5669.9932
                                  
                                  
so,Sample Size required=       5670