Answer:
The confidence coefficient was approximately [tex]z = 1.75[/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 coefficient [tex]z[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
The lower end of the interval is given by:
[tex]L = \pi - z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
The upper end of the interval is given by:
[tex]U = \pi + z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
We have that:
The value of [tex]\pi[/tex] is the midway point between the lower and the upper end. So
[tex]\pi = \frac{0.372 + 0.458}{2} = 0.415[/tex]
The upper end is 0.458. So we can find z
[tex]U = \pi + z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.458 = 0.415 + z\sqrt{\frac{0.415*(1-0.415)}{400}}[/tex]
[tex]0.0246z = 0.08[/tex]
[tex]z = 1.75[/tex]
