Question

: Consider the test of H0 : p = 0.7 Vs. Ha : µ > 0.7 using a random sample of 400 values and α = 1%. Find the power of the test when pa = 0.75.

Answer 1

The power of the test is computed as the probability of rejecting the null hypothesis when it is false Here as this is a one tailed test, we get from the standard normal tables,
P(Z > 2.326) = 0.01

Therefore the critical p - value here is computed as:

Therefore now we are rejecting the null hypothesis here when p >= 0.7533

Therefore the power of the test given the true proportion is 0.75 is computed here as:

P( p > 0.7533)

Converting it to a standard normal variable, we get here:

Getting it from the standard normal tables, we get here:

Therefore 43.94% is the required power of the test here.