Question

pt 9.1.17 Construct a 90% confidence interval of the population proportion using the given information. x= 105, n = 150 Click here to view the table of critical values. The lower bound is The upper bound is (Round to three decimal places as needed.) Enter your answer in the edit, fields and then click Check Answer, All parts showing

Answer 1

solution:
Given that, n=150, X=105
p^=X/n
= 105/150
= 0.7
The best point estimate of population proportion p is p^= 0.7
(1–α)%=90%
(1–α)=0.90
α=0.10
α/2=0.05
Zα/2=1.645 ....... from standard normal table.
Margin of error=E=Zα/2 ×√{[p^(1-p^)]/n}
=1.645 ×√{[0.7(1-0.7)]/150}
=1.645 × 0.0374
= 0.0615
Margin of error=E=0.0615
90% Confidence Interval for true population proportion p is given as,
p^ ± Margin of error
=(0.7-0.0615,0.7+0.0615)
=(0.6385,0.7615)
=(0.638,0.761)....upto 3 decimal.
The lower bound is 0.638
The upper bound is 0.761