Question

You are interested in estimating the the mean age of the citizens living in your community....

You are interested in estimating the the mean age of the citizens living in your community. In order to do this, you plan on constructing a confidence interval; however, you are not sure how many citizens should be included in the sample. If you want your sample estimate to be within 3 years of the actual mean with a confidence level of 97%, how many citizens should be included in your sample? Assume that the standard deviation of the ages of all the citizens in this community is 24 years.

Homework Answers

Answer #1

Solution

standard deviation =   =24

Margin of error = E = 3

At 97% confidence level the z is ,

= 1 - 97% = 1 - 0.97 = 0.03

/ 2 = 0.03 / 2 = 0.015

Z/2 = Z0.015 = 2.17

sample size = n = [Z/2* / E] 2

n = ( 2.17*24 / 3 )2

n =301.3696

Sample size = n =301 rounded

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
You are interested in estimating the the mean age of the citizens living in your community....
You are interested in estimating the the mean age of the citizens living in your community. In order to do this, you plan on constructing a confidence interval; however, you are not sure how many citizens should be included in the sample. If you want your sample estimate to be within 4 years of the actual mean with a confidence level of 97%, how many citizens should be included in your sample? Assume that the standard deviation of the ages...
interested in estimating the mean age of the citizens living in your community in order to...
interested in estimating the mean age of the citizens living in your community in order to do this your plan on constructing a confidence interval however you are not show how many citizens should be included in the sample if you want your sample estimate to be within 4 years of the actual name with a confidence level of 96% how many citizens should be included in your sample as long that the standard deviation of the ages of all...
For a certain group of cancer patients we are interested in estimating the mean age of...
For a certain group of cancer patients we are interested in estimating the mean age of diagnosis. We would like a 95% confidence level. Assume the population standard deviation is 12 years. a. What sample size do you recommend for an interval width of 5 years? b. What sample size do you recommend for an interval width of 2 years?
The following data is the results of a random sample of the ages (in years) of...
The following data is the results of a random sample of the ages (in years) of 12 houses in a community: 18, 22, 23, 19, 18, 24, 26, 20, 17, 12, 27, 28. Assume the population is normal. Construct a 90% confidence interval for the mean age of a house in this community. a) (18.8, 23.5) b) (18.7, 23.6) c) (18.9, 23.4) d) (19.0, 23.3) 7. If you want to estimate the mean age of a house in the community...
You are interested in estimating the the mean weight of the local adult population of female...
You are interested in estimating the the mean weight of the local adult population of female white-tailed deer (doe). From past data, you estimate that the standard deviation of all adult female white-tailed deer in this region to be 39 pounds. What sample size would you need to in order to estimate the mean weight of all female white-tailed deer, with a 98% confidence level, to within 5 pounds of the actual weight? (Use Excel to find the appropriate critical...
SAT scores are distributed with a mean of 1,500 and a standard deviation of 300. You...
SAT scores are distributed with a mean of 1,500 and a standard deviation of 300. You are interested in estimating the average SAT score of first year students at your college. If you would like to limit the margin of error of your 95% confidence interval to 25 points, how many students should you sample? Make sure to give a whole number answer.
SAT scores are distributed with a mean of 1,500 and a standard deviation of 300. You...
SAT scores are distributed with a mean of 1,500 and a standard deviation of 300. You are interested in estimating the average SAT score of first year students at your college. If you would like to limit the margin of error of your 95% confidence interval to 25 points, how many students should you sample? Make sure to give a whole number answer.
SAT scores are distributed with a mean of 1,500 and a standard deviation of 300. You...
SAT scores are distributed with a mean of 1,500 and a standard deviation of 300. You are interested in estimating the average SAT score of first year students at your college. If you would like to limit the margin of error of your 95% confidence interval to 25 points, how many students should you sample? Make sure to give a whole number answer.
A decision maker is interested in estimating the mean of a population based on a random...
A decision maker is interested in estimating the mean of a population based on a random sample. She wants the confidence level to be 90​% and the margin of error to be ±0.50 She does not know what the population standard deviation​ is, so she has selected the pilot sample below. Based on this pilot​ sample, how many more items must be sampled so that the decision maker can make the desired confidence interval​ estimate? 8.50 4.87 10.95 15.05 14.78...
5. A manufacturer of college textbooks is interested in estimating the strength of the bindings produced...
5. A manufacturer of college textbooks is interested in estimating the strength of the bindings produced by a particular binding machine. Strength can be measured by recording the force required to pull the pages from the binding. If this force is measured in pounds, how many books should be tested in order to estimate with 95% confidence to within 0.1 lb the average force required to break the binding? Assume that  is known to be .8 lb. 6. We...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT