Respuesta :
Answer:
The confidence interval has a lower limit of 0.546 and an upper limit of 0.675.
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].
In 2017, a random sample of 154 individuals who graduated from high school 12 months prior was selected. From this sample, 94 students were found to be enrolled in college or a trade school.
This means that [tex]n = 154, \pi = \frac{94}{154} = 0.6104[/tex]
90% confidence level
So [tex]\alpha = 0.1[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.1}{2} = 0.95[/tex], so [tex]Z = 1.645[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.6104 - 1.645\sqrt{\frac{0.6104*0.3896}{154}} = 0.546[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.6104 + 1.645\sqrt{\frac{0.6104*0.3896}{154}} = 0.675[/tex]
The confidence interval has a lower limit of 0.546 and an upper limit of 0.675.
