Respuesta :
Answer:
The minimum sample size required to create the specified confidence interval is of 565.
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.8}{2} = 0.1[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.1 = 0.9[/tex], so Z = 1.28.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
Found the standard deviation to be 1.3.
This means that [tex]\sigma = 1.3[/tex]
Error of no more than 0.07. What is the minimum sample size required to create the specified confidence interval?
This is n for which M = 0.07. So
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]0.07 = 1.28\frac{1.3}{\sqrt{n}}[/tex]
[tex]0.07\sqrt{n} = 1.28*1.3[/tex]
[tex]\sqrt{n} = \frac{1.28*1.3}{0.07}[/tex]
[tex](\sqrt{n})^2 = (\frac{1.28*1.3}{0.07})^2[/tex]
[tex]n = 565.1[/tex]
Rounding up:
The minimum sample size required to create the specified confidence interval is of 565.
