The melting point of each of 16 samples of a certain brand o

The melting point of each of 16 samples of a certain brand of hydrogenated vegetable oil was determined, resulting in a sample mean of 94.32. Assume that the distribution of melting point is normal with = 1.20.

If a level .01 test is used, what is (94), the probability of type II error when =94?

Solution

We first get the z score for the critical value. As z = (x - u) sqrt(n) / s, then as          
          
x = critical value =    94.32      
u = mean =    94      
n = sample size =    16      
s = standard deviation =    1.2      
          
Thus,          
          
z = (x - u) * sqrt(n) / s =    1.066666667      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   1.066666667   ) =    0.143061192 [ANSWER]