Explore Westonci.ca, the leading Q&A site where experts provide accurate and helpful answers to all your questions. Explore in-depth answers to your questions from a knowledgeable community of experts across different fields. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.
Sagot :
Answer:
0.0101 < p < 0.1499
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 zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
Out of 100 adult residents sampled, 8 had kids. Based on this, construct a 99%.
This means that [tex]n = 100, \pi = \frac{8}{100} = 0.08[/tex]
99% confidence level
So [tex]\alpha = 0.01[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.01}{2} = 0.995[/tex], so [tex]Z = 2.575[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.08 - 2.575\sqrt{\frac{0.08*0.92}{100}} = 0.0101[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.08 + 2.575\sqrt{\frac{0.08*0.92}{100}} = 0.1499[/tex]
Express your answer in tri-inequality form.
0.0101 < p < 0.1499
Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Find reliable answers at Westonci.ca. Visit us again for the latest updates and expert advice.
