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Confidence interval for hospital patients

You take a sample of 200 patients from a hospital floor and find the average length of stay is 3 days with a standard deviation of 1 day. What is the 95% confidence interval on the population mean? (Check answer: 2.8614 to 3.1386)

What would the interval be if you had actually taken a sample of 400? (Assume the sample mean is still 3. In actual practice it would change with a different sample size, of course. Why?) (Check answer: 2.9020 to 3.0980)

What if the sample size were 50, assuming again that the sample mean did not change? (Check answer 2.7228 to 3.2772)

What happened to the interval? Why?

What would happen with the average stay of 3 days, standard deviation of 1,if I want to be 99.73% confident? Again assume the same sample mean. (Verify that z would be 3.00)

Check answers:

N
Low
High

200
3 - .2121
3 + .2121

400
3 - .1500
3 + .1500

50
3 - .4243
3 + .4243

Why did the ranges increase?

What would happen with the average stay of 3 days, standard deviation of 1 if I used a confidence level of 11.92% (Verify that z=0.15)

Check answers:

N
Low
High

200
3 - .0106
3 + .0106

400
3 - .0075
3 + .0075

50
3 - .0212
3 + .0212

Why did the ranges decrease?
How would you feel if someone said that there was an 11.92% chance that the interval contained the actual population mean?

Solution Preview

I have attached the solution.

You take a sample of 200 patients from a hospital floor and find the average length of stay is 3 days with a standard deviation of 1 day. What is the 95% confidence interval on the population mean? (Check answer: 2.8614 to 3.1386)

Here N = 200
Mean = 3
Standard deviation = 1
 95 % Confidence interval =

What would the interval be if you had actually taken a sample of 400? (Assume the sample mean is still 3. In actual practice it would change with a different sample size, of course. Why?) (Check ...

Solution Summary

This solution determines the sample, mean, standard deviation, confidence interval and comments on how changes in population affect the confidence interval.

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