Answer:
a) A sample size of at least 251 students is needed.
b) A sample of at least 97 students is needed.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of , and a confidence level of , we have the following confidence interval of proportions.
In which
z is the zscore that has a pvalue of .
The margin of error is:
95% confidence level
So , z is the value of Z that has a pvalue of , so .
(a) you are unwilling to predict the proportion value at your school
We need a sample size of at least n.
n is found when M = 0.08.
We wont predict a proportion value for the school, so we use
So
Rounding up
A sample size of at least 251 is needed.
(b) you use the results from the surveyed school as a guideline.
Now we have that
So
Rounding up
A sample of at least 97 students is needed.