Westonci.ca is the ultimate Q&A platform, offering detailed and reliable answers from a knowledgeable community. Our Q&A platform provides quick and trustworthy answers to your questions from experienced professionals in different areas of expertise. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.
Sagot :
Answer:
A sample size of 392 is required.
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].
The margin of error is:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
18% of students struggle in their classes because they don't spend more than 8 hours studying independently outside of a 4-unit class.
This means that [tex]\pi = 0.18[/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].
You would like to be 99% confident that your estimate is within 5% of the true population proportion. How large of a sample size is required?
A sample size of n is required.
n is found when M = 0.05. So
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.05 = 2.575\sqrt{\frac{0.18*0.82}{n}}[/tex]
[tex]0.05\sqrt{n} = 2.575\sqrt{0.18*0.82}[/tex]
[tex]\sqrt{n} = \frac{2.575\sqrt{0.18*0.82}}{0.05}[/tex]
[tex](\sqrt{n})^2 = (\frac{2.575\sqrt{0.18*0.82}}{0.05})^2[/tex]
[tex]n = 391.5[/tex]
Rounding up:
A sample size of 392 is required.
Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. We're glad you chose Westonci.ca. Revisit us for updated answers from our knowledgeable team.