The proportion of families who buy milk from Publix in Tampa is assumed to be p = 0.6. If a random sample of 10 families show that 3 or less buy milk from Publix, we shall reject the null hypothesis p =0.6 in favor of the alternative hypothesis p < 0.6.

a) Find the probability of a type I error α if the true proportion is p=0.6.

b) Evaluate the probability of a type II error (β) if the true value of p is equal to the following:

i) P = 0.3, 
ii) P = 0.4
iii) p = 0.5