Answer:
90% of confidence interval for the true population of club members who use compost
(0.44424 , 0.45576)
Step-by-step explanation:
Step(i):-
Given that the size of the sample 'n' =200
Given that the sample proportion
p = 45% = 0.45
Level of significance = 90% or 10%
Critical value Z₀.₁₀ = 1.645
Step(ii):-
90% of confidence interval for the true population of club members who use compost
[tex](p^{-} - Z_{0.10} \sqrt{\frac{p(1-p^{-} )}{n} } , p^{-} + Z_{0.10} \sqrt{\frac{p(1-p^{-} )}{n} })[/tex]
[tex]((0.45 - 1.645\sqrt{\frac{0.45(1-0.45)}{200} } , 0.45 + 1.645\sqrt{\frac{0.45(1-0.45)}{200} })[/tex]
(0.45 - 0.00576 , 0.45 +0.00576)
(0.44424 , 0.45576)
Final answer:-
90% of confidence interval for the true population of club members who use compost
(0.44424 , 0.45576)
