Management is contemplating selling the company's products through the internet. Before a decision is made, several studies will have to be carried out. One of them is to estimate the proportion of adult Georgian who have access to the internet at home. A survey is carried out. We find that out of 800 randomly interviewed adult Georgian, 330 have access to the internet.

a) Further to the survey results, would management be correct in concluding that more than 40% of adult Georgian s have access to the internet? (Carry out a test of hypothesis using a significance level of 1%)

b) Compute the power of the previous test if the true proportion of adults having access to the internet in the population is 41%. What is the power if the true proportion is 42%? 43%? 44%? 45%? Redo the computations for α = 10%. What do we notice?