Margin of Error and Corresponding Confidence Levels
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1. Assume that a randm sample is used to estimate a popultion proportion p. Find the margin of error E that corresponds to the given statistics and confidence level.
98% confidence; the sample size is 1206, of which 35% are successes
The margin of error E= ______ (round to four decimal places as needed)
2. Use the given data to find the minimum sample size required to estimate a population proportion or percentage.
Margin of error: 0.01; confidence level 95%; ^p and ^q unknown
n=________ (round up to the nearest integer.)
3. 9) Randomly selected students participated in a experiment to test their ability to determine when on minute (or sixty seconds) has passed. Forty students yielded a sample mean of 58.8 seconds. Assuming that ?=10.2 seconds, construct and interpret a 99% confidence interval estimate of the population mean of all students.
What is the 99% confidence interval for the population mean µ?
___<µ<___ (Type integers or decimals rounded to one decimal place as needed.)
Based on the result, is it likely that the students' estimates have a mean that is reasonably close to sixty seconds?
a) Yes, because the confidence interval does not include sixty seconds.
b) No, because the confidence interval does not include sixty seconds.
c) Yes, because the confidence interval includes sixty seconds.
d) No, because the confidence interval includes sixty seconds.
4. A data set includes 104 body temperatures of healthy adult humans for which x=98.1 F and s=0.53F.
a) what is the best point estimate of the mean body temperature of all healthy humans?
The best point estimate is _____ F
b) using the sampe statistics, construct a 90% confidenc interval estimate of the mean body temperature of all healthy humans. Do the confidenc interval limits contain 98.6F? what does the sample suggest about the use of 98.6F as the mean body temperature?
What is the confidence interval estimate of the popultion mean u?
_____F<u<____F
do the confidenc interval limits contain 98.6F
Yes ____
No ____
What does this suggest about the use of 98.6F as the mean body temperature?
a. this suggests that the mean body temperature could be higher than 98.6F
b. this suggests that the mean body temperature could be lower than 98.6F
c. This suggests that the mean body temperature could very possibly be 98.6F.
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Solution Summary
The solution determines the margin of error and corresponding confidence levels.
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1. E=Z(alpha/2)*sqrt(p*(1-p)/n)=2.326*sqrt(0.35*0.65/1206)=0.0319
2. default p=q=0.5
E=z(alpha/2)*sqrt(p*(1-p)/n)
0.01=1.96*sqrt(0.5*0.5/n)
n=(1.96/0.01)^2*0.25=9604
3. E=Z(alpha)*standard ...
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