Answer :
Answer:
Lower bound: 0.2497 = 24.97%
Upper bound: 0.3503 = 35.03%
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 zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
For this problem, we have that:
A random sample of 350 voters from Delaware finds that 105 of them intend to vote for Bill McNeely in an upcoming election for Governor. This means that [tex]n = 350, p = \frac{105}{350} = 0.3[/tex]
96% confidence level
So [tex]\alpha = 0.04[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.04}{2} = 0.98[/tex], so [tex]Z = 2.055[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.3 - 2.055\sqrt{\frac{0.3*0.7}{350}} = 0.2497[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.3 + 2.055\sqrt{\frac{0.3*0.7}{350}} = 0.3503[/tex]