If If you are a researcher and would like to control the sig

   If If you are a researcher and would like to control the significance level at 0.025 and at 0.01  for testing whether there is a significant difference in a process mean given that process is known to be N(,25) He formulated his test as follows:   H₀ : µ = 19   H_A: µ =  21.   What sample size does

he need?

Solution

z for 0.025 level = -1.96.....

now, (c- 19) / ( 5 / sqrt(n) ) = -1.96...
or, c = 19+( -9.8 / sqrt(n) )
so, beta = 1 - p( z > (19+( -9.8 / sqrt(n) ) - 21) / (5 / sqrt(n) ) = 1 - p( z> ( [-2 sqrt(n)/5] - 1.96 )

or, 0.01 = p( z <=  ( [-2 sqrt(n)/5] - 1.96 ) or, -2.326 =  ( [-2 sqrt(n)/5] - 1.96 )
or, n = 1 (approx)......he needs to use a single observation to maintain this limits!