Question

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. What is 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

Answer 1

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 $\pi$, and a confidence level of $1-\alpha$, we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the z-score that has a p-value of $1 - \frac{\alpha}{2}$.

95% confidence level

So $\alpha = 0.05$, z is the value of Z that has a p-value of $1 - \frac{0.05}{2} = 0.975$, so $Z = 1.96$.

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 $n = 234, \pi = \frac{48}{234} = 0.2051$

The upper limit of this interval is:

$\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2051 + 1.96\sqrt{\frac{0.2051*0.7949}{234}} = 0.2568$

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.