Question

Question 1

Answer 1

Using the z-distribution, it is found that the 90% confidence interval for the proportion of Americans who believe that the minimum wage should  be raised is (0.4689, 0.5311).

Confidence interval of a proportion

• In a sample with a number n of people surveyed with a probability of a success of $\pi$, and a confidence level of $\alpha$, 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 $\frac{1+\alpha}{2}$.

In this problem:

• 350 out of 700 in the sample said yes, hence $n = 700, \pi = \frac{350}{700} = 0.5$.

• 90% confidence level, hence$\alpha = 0.9$, z is the value of Z that has a p-value of $\frac{1+0.9}{2} = 0.95$, so $z = 1.645$.

The lower limit of this interval is:

$\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.5 - 1.645\sqrt{\frac{0.5(0.5)}{700}} = 0.4689$

The upper limit of this interval is:

$\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.5 + 1.645\sqrt{\frac{0.5(0.5)}{700}} = 0.5311$

The 90% confidence interval for the proportion of Americans who believe that the minimum wage should  be raised is (0.4689, 0.5311).

To learn more about the z-distribution, you can take a look at brainly.com/question/26130512