Answer :
Answer:
The upper bound of a 95% confidence interval for the proportion of individuals over the age of 25 in Oregon who do not have a high school diploma is of 0.2568.
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].
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].
In a sample of 234 individuals over the age of 25, chosen at random from the state of Oregon, 48 did not have a high school diploma.
This means that [tex]n = 234, \pi = \frac{48}{234} = 0.2051[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2051 + 1.96\sqrt{\frac{0.2051*0.7949}{234}} = 0.2568[/tex]
The upper bound of a 95% confidence interval for the proportion of individuals over the age of 25 in Oregon who do not have a high school diploma is of 0.2568.