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Answer:
A sample size of 1031 is required.
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 of:
37% of freshmen do not visit their counselors regularly.
This means that
98% confidence level
So , z is the value of Z that has a pvalue of
, so
.
You would like to be 98% confident that your estimate is within 3.5% of the true population proportion. How large of a sample size is required?
A sample size of n is required.
n is found when M = 0.035. So
Rounding up:
A sample size of 1031 is required.
We can write the sequence out more fully, as we can see each time it is divided by 6.
60, 60/6, 60/6^2, 60/6^3, and so on.
Therefore we know the sequence can be written as
You can think of this as a graph, i.e. y=60/6^(x-1)
As a result, as x tends to infinity, y tends to 0 (since it effectively becomes 60/infinity). Therefore the sequence converges toward zero.
60, 60/6, 60/6^2, 60/6^3, and so on.
Therefore we know the sequence can be written as
You can think of this as a graph, i.e. y=60/6^(x-1)
As a result, as x tends to infinity, y tends to 0 (since it effectively becomes 60/infinity). Therefore the sequence converges toward zero.