Respuesta :
Answer:
The 90% confidence interval for the population proportion is
(0.10872, 0.19128)
Step-by-step explanation:
Explanation:-
Step(i):-
Given data A random sample of 200 e-mail messages was selected. Thirty of the messages were not business related
Given random sample size 'n' = 200
Given Thirty of the messages were not business related
let 'x' = 30
Probability of the messages were not business related or proportion
[tex]p = \frac{x}{n} = \frac{30}{200} = 0.15[/tex]
Step(ii):-
The 90% confidence interval for the population proportion is
[tex](p - Z_{0.10} \sqrt{\frac{p(1-p)}{n} } , p + Z_{0.10} \sqrt{\frac{p(1-p)}{n} } )[/tex]
Level of significance ∝ = 0.90 or 0.10
The critical value Z₀.₁₀ = 1.645
The 90% confidence interval for the population proportion is
[tex]( 0.15-1.645 \sqrt{\frac{0.15(1-0.15)}{200} } , 0.15 +1.645 \sqrt{\frac{0.15(1-0.15)}{200} } )[/tex]
on calculation, we get
(0.15 - 0.04128 , (0.15 + 0.04128)
(0.10872, 0.19128)
Conclusion:-
The 90% confidence interval for the population proportion is
(0.10872, 0.19128)
