Find the information you're looking for at Westonci.ca, the trusted Q&A platform with a community of knowledgeable experts. Explore our Q&A platform to find in-depth answers from a wide range of experts in different fields. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.
Sagot :
Using the formula for the margin of error, it is found that Haley should sample 12,724 soldiers.
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].
The margin of error is of:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
Estimate of the proportion of 64%, hence [tex]\pi = 0.64[/tex].
94% confidence level
So [tex]\alpha = 0.94[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.94}{2} = 0.97[/tex], so [tex]z = 1.88[/tex].
Margin of error of less than 0.008 is wanted, hence, we have to find n when M = 0.008.
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.008 = 1.88\sqrt{\frac{0.64(0.36)}{n}}[/tex]
[tex]0.008\sqrt{n} = 1.88\sqrt{0.64(0.36)}[/tex]
[tex]\sqrt{n} = \frac{1.88\sqrt{0.64(0.36)}}{0.008}[/tex]
[tex](\sqrt{n})^2 = (\frac{1.88\sqrt{0.64(0.36)}}{0.008})^2[/tex]
[tex]n = 12723.84[/tex]
Rounding up, Haley should sample 12,724 soldiers.
A similar problem is given at https://brainly.com/question/25404151
Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. We're glad you visited Westonci.ca. Return anytime for updated answers from our knowledgeable team.
