Question

41.

Answer 1

a) ( 0.8509718, 0.8890282)

b) ( 0.7255, 0.7745)

Explanation:

(a)

Given that , a = 0.05, Z(0.025) =1.96 (from standard normal table)

So Margin of error = Z × sqrt(p × (1-p)/n) = 1.96 × sqrt(0.87 × (1-0.87) / 1200)

=0.01902816

So 95 % confidence interval is

p+/-E  

0.87+/-0.01902816  

( 0.8509718, 0.8890282)

(b)

Margin of error = 1.96 × sqrt (0.75 × (1-0.75) / 1200) = 0.0245

So 95% confidence interval is

p+/-E

0.75+/-0.0245

( 0.7255, 0.7745)