Respuesta :
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 [tex]\pi[/tex], and a confidence level of [tex]\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]\frac{1+\alpha}{2}[/tex].
In this problem:
- 350 out of 700 in the sample said yes, hence [tex]n = 700, \pi = \frac{350}{700} = 0.5[/tex].
- 90% confidence level, hence[tex]\alpha = 0.9[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.9}{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}} = 0.5 - 1.645\sqrt{\frac{0.5(0.5)}{700}} = 0.4689[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.5 + 1.645\sqrt{\frac{0.5(0.5)}{700}} = 0.5311[/tex]
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 https://brainly.com/question/26130512
