Download Chap 14 Lesson 3 - Spring

Chapter 14: Choosing the Sample Size
Experimenters can arrange to have both high confidence and a small margin of
error by taking a large enough number of observations for their sample. If they
know what margin of error they are hoping to achieve, the following formula can
be used to determine the number of observations they need to do so:


nz*
 m 
2
= sample size needed for specified margin of error m
 the formula may lead to a sample size that is not feasible to accomplish so
it is not a guarantee to stronger results
 the size of the population the sample is coming from does not influence
the size of the sample or the margin of error in any way
 ALWAYS ROUND UP TO NEXT HIGHER WHOLE NUMBER FOR n!!!
Example 14.5 (page 355)
The biologists from our previous newt example would like to estimate the mean
healing rate µ within no more than ±3 micrometers per hour with 90%
confidence. How many newts must they measure? (Recall σ = 8)
Exercise 14.9 (p. 355)
How large a sample of high school students would be needed to estimate the
mean change µ in SAT score to within ±2 points with 95% confidence? (σ = 50)
Exercise 14.10 (p. 356)
How large a sample of schoolgirls would be needed to estimate the mean IQ
score µ within ±5 points with 90% confidence? (σ = 15)
Finding Sample Size Homework
1. A cheese processing company wants to estimate the mean cholesterol content of oneounce servings of cheese. The estimate must be within 0.5 milligram of the population mean.
Determine the minimum required sample size to construct a 95% confidence interval for the
population mean if the standard deviation is 2.8 milligrams.
Repeat the problem using a 99% confidence interval.
Which level of confidence requires a larger sample size?
Why do you think that is the case?
2. A paint manufacturer uses a machine to fill gallon cans with paint. The manufacturer
wants to estimate the mean volume of paint the machine is putting in the cans within 0.25
ounce. Determine the minimum sample size required to construct a 90% confidence interval
for the population mean if the standard deviation is 0.85 ounce.
Repeat the problem using an error tolerance of 0.15 ounce.
Which error tolerance requires a larger sample size?
Why do you think this is the case?
3. A soccer ball manufacturer wants to estimate the mean circumference of soccer balls
within 0.1 inch. Determine the minimum required sample size to construct a 99% confidence
interval for the population mean if the standard deviation is 0.25 inch.
Repeat the problem using a standard deviation of 0.3 inch.
Which standard deviation requires a larger sample size?
Why do you think this is the case?