Answer:
n = 217
Step-by-step explanation:
For 95% confidence, z = 1.96
Population standard deviation = 15
E = 2
Hence,
Number of Foothill College students required for survey
n = (\frac{1.96*15}{2})^2
n = 216.09
n = 217 [Rounded off to next whole number]
Answer:
We need to survey at least 217 students.
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{1-0.95}{2} = 0.025[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].
So it is z with a pvalue of [tex]1-0.025 = 0.975[/tex], so [tex]z = 1.96[/tex]
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.
How many randomly selected Foothill College students must be surveyed?
We need to survey at least n students.
n is found when [tex]\sigma = 15, M = 2[/tex]. So
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
[tex]2 = 1.96*\frac{15}{\sqrt{n}}[/tex]
[tex]2\sqrt{n} = 1.96*15[/tex]
[tex]\sqrt{n} = \frac{1.96*15}{2}[/tex]
[tex](\sqrt{n})^{2} = (\frac{1.96*15}{2})^{2}[/tex]
[tex]n = 216.09[/tex]
Rounding up
We need to survey at least 217 students.
