Respuesta :
Answer:
The critical value that corresponds to a confidence level of 97.1% is [tex]Z = 2.18[/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].
97.1% confidence level
So [tex]\alpha = 0.029[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.029}{2} = 0.9855[/tex], so [tex]Z = 2.18[/tex].
The critical value that corresponds to a confidence level of 97.1% is [tex]Z = 2.18[/tex].
