Download Desired Sample Size

AP Statistics
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When calculating a sample size for a desired
margin of error, the only thing that can be
controlled is “n”.
  
m = margin of error
m  z *

 n
We want:
  
m  z *

 n
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A drug-maker analyses a specimen from each
batch of a product. The results of repeated
measurements follow a normal distribution
quite closely. The standard deviation of this
distribution is known to be σ = .0068 grams per
liter.
How many samples of the product must be
tested to give a margin of error of +/- .005
grams per liter with a 95% confidence?


σ = .0068 z* = 1.960 (95% confidence level)
Desired margin of error = +/- .005 = m


.0068
.005  1.960 

n

.005  .013328
n
.005 n  .013328
 n
2
  2.6656 
2
n  7.105 so take 8 (always bump up!)
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Predict a school’s IQ score within 5 points and
be 99% confident. What sample size do you
need?
IQ is N(100,15) z* = 2.576 m = 5


15
5  2.576 

n

5  38.64
n
5 n  38.64
 n
2
  7.728
2
n  59.72 or 60 (again, bump up!)
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Company management wants a report of the
mean screen tension for today’s production
accurate to within +/- 5mV with a 95%
confidence.
How large a sample of video monitors must be
measured to comply with this request?
Assume σ = 43.
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The point estimate, x-bar, must be calculated
from an SRS for the results to generalize.
Outliers can have a big effect on confidence
intervals. Check for these graphically.
When the population is non-normal, the
Central Limit Theorem is important (n ≥ 30).
You must know σ from the population.
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Use stemplots, histograms, or normal
probability plots to assess normality of sample
data.
Know your assumptions.
Be able to calculate and interpret a Level-C
confidence interval.
Be able to calculate desired sample size.
Do formal write-ups with complete sentences.
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Textbook 10.12 - 10.18