Answer:
94 more students should be included in the sample.
Step-by-step explanation:
We have that to find our
level, that is the subtraction of 1 by the confidence interval divided by 2. So:
Now, we have to find z in the Ztable as such z has a pvalue of
.
So it is z with a pvalue of
, so
Now, find the margin of error M as such
In which
is the standard deviation of the population and n is the size of the sample.
How many students we need to sample to be 99% sure that the sample mean x is within 1 semester hour of the population mean?
We need to survey n students.
n is found when M = 1.
We have that ![\sigma = 4.7](https://tex.z-dn.net/?f=%5Csigma%20%3D%204.7)
So
![\sqrt{n} = 2.575*4.7](https://tex.z-dn.net/?f=%5Csqrt%7Bn%7D%20%3D%202.575%2A4.7)
![(\sqrt{n})^{2} = (2.575*4.7)^{2}](https://tex.z-dn.net/?f=%28%5Csqrt%7Bn%7D%29%5E%7B2%7D%20%3D%20%282.575%2A4.7%29%5E%7B2%7D)
![n = 146.47](https://tex.z-dn.net/?f=n%20%3D%20146.47)
Rounding up
147 students need to be surveyed.
How many more students should be included...?
53 have already been surveyed
147 - 53 = 94
94 more students should be included in the sample.