Answer:
95% confidence interval for a Population proportion
0.6937 ≤ P ≤ 0.7515
Step-by-step explanation:
Explanation:-
Given sample size 'n' = 238
probability of successes or sample proportion
[tex]p = \frac{x}{n} = \frac{172}{238} =0.7226[/tex]
95% confidence interval for a Population proportion is determined by
[tex](p^{-} - Z_{0.05} \sqrt{\frac{p(1-p)}{n} } , p^{-} + Z_{0.05} \sqrt{\frac{p(1-p)}{n} })[/tex]
[tex](0.7226 - 1.96\sqrt{\frac{0.7226(1-0.7226)}{238} } , 0.7226+ 1.96\sqrt{\frac{0.7226(1-0.7226)}{238} })[/tex]
(0.7226 - 0.0289 , 0.7226 + 0.0289)
(0.6937 , 0.7515)
Conclusion:-
95% confidence interval for a Population proportion
0.6937 ≤ P ≤ 0.7515
