Ben uses a compass and a straightedge to bisect angle PQR, as shown below: The figure shows two rays QP and QR with a common end
point Q. An arc drawn from Q cuts the ray QP at A and the ray QR at B. Two small arcs intersect between the lines QP and QR. The point of intersection of the arcs is labeled S. The points Q, S, and T are joined with a line. Which statement best explains why Ben uses the same width to draw arcs from A and B that intersect at S? BQ = BS when ∠AQS ≅ ∠BQS. AQ = AS when ∠AQS ≅ ∠BQS. ∠AQS ≅ ∠BQS when AS = BS and AQ = BQ. ∠AQS ≅ ∠BQS when AS = BQ and BS = AQ.
2 answers:
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Answer:
a) The minimum sample size is 601.
b) The minimum sample size is 2401.
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:
For this problem, we have that:
We dont know the true proportion, so we use , which is when we are are going to need the largest sample size.
95% confidence level
So , z is the value of Z that has a pvalue of
, so
.
a. If a 95% confidence interval with a margin of error of no more than 0.04 is desired, give a close estimate of the minimum sample size that will guarantee that the desired margin of error is achieved. (Remember to round up any result, if necessary.)
This is n for which M = 0.04. So
Rounding up
The minimum sample size is 601.
b. If a 95% confidence interval with a margin of error of no more than 0.02 is desired, give a close estimate of the minimum sample size necessary to achieve the desired margin of error.
Now we want n for which M = 0.02. So
The minimum sample size is 2401.