Exercise 10.8
(a) One must test the hypothesis that a sampling proportion is less that 3%, if the real one in 5%.
Under H0 , Z = (p̂ -p) ⁄ √ p(1-p)/N is approximately N(0,1). Here p= 0.05.
We need to compute P( p̂ < .03 | p̂ < .05 ), since already know that the sample proportion is less than 5%.
The P-value of the test is : 35.8795%
(b) The solution is to increase the sample size. For example, with N=1000, the P-value of the test on the proportion would have been 0.3709%
Thus, for example, we would have concluded that the true proportion is significantly smaller than 5%.