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Sagot :
Answer:
The 95% confidence interval is [tex]0.231 \pm 1.96\sqrt{\frac{0.231*0.769}{432}}[/tex]
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
A random sample of 432 voters revealed that 100 are in favor of a certain bond issue.
This means that [tex]n = 432, \pi = \frac{100}{432} = 0.231[/tex]
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
Confidence interval:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.231 \pm 1.96\sqrt{\frac{0.231*0.769}{432}}[/tex]
The 95% confidence interval is [tex]0.231 \pm 1.96\sqrt{\frac{0.231*0.769}{432}}[/tex]
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