Get reliable answers to your questions at Westonci.ca, where our knowledgeable community is always ready to help. Join our Q&A platform to get precise answers from experts in diverse fields and enhance your understanding. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.
Sagot :
Answer:
A sample of [tex]n = (\frac{1.96\sqrt{0.3696*0.6304}}{E})^2[/tex] is needed, in which E is the desired margin of error, as a proportion. If we find a decimal value, we round up to the next whole number.
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 of:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In a previous study of 1012 randomly chosen respondents, 374 said that there should be such a law.
This means that [tex]n = 1012, \pi = \frac{374}{1012} = 0.3696[/tex]
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
How large a sample size is needed to be 95% confident with a margin of error of E?
A sample size of n is needed, and n is found when M = E.
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]E = 1.96\sqrt{\frac{0.3696*0.6304}{n}}[/tex]
[tex]E\sqrt{n} = 1.96\sqrt{0.3696*0.6304}[/tex]
[tex]\sqrt{n} = \frac{1.96\sqrt{0.3696*0.6304}}{E}[/tex]
[tex](\sqrt{n})^2 = (\frac{1.96\sqrt{0.3696*0.6304}}{E})^2[/tex]
[tex]n = (\frac{1.96\sqrt{0.3696*0.6304}}{E})^2[/tex]
A sample of [tex]n = (\frac{1.96\sqrt{0.3696*0.6304}}{E})^2[/tex] is needed, in which E is the desired margin of error, as a proportion. If we find a decimal value, we round up to the next whole number.
We hope this was helpful. Please come back whenever you need more information or answers to your queries. Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Thank you for using Westonci.ca. Come back for more in-depth answers to all your queries.
