# Small Sample size Confidence Intervals

Health insurers and the federal government are both putting pressure on hospitals to shorten the average length of stay (LOS) of their patients. The average LOS for men in the US is 5.2 days and the average for women is 4.5. A random sample of 20 hospitals in one state had a mean LOS for women of 3.8 days and a standard deviation of 1.2 days...

a) use a 95% confidence interval to estimate the population mean LOS for women in the state's hospital:

$$3.8 \pm 2.093(1.2/\sqrt{20}).$$

These are the numbers that I've gotten, but I'm not sure where these numbers come from. My professor just kinda threw em at us.

b) conduct a test at a=.05 to determine if the average LOS for women in the state is equal to that of the national average.

I know how to do population for these types of answers, but I'm not sure how to do samples.

c) What happens to a confidence interval as it gets smaller or large?

Sorry for such a long post, but I have a final coming up and I'm looking for some help. Any help, links, or even taking the time to look at this question I truly appreciate. Best Wishes to all and have a good day

• Have you written down the whole problem. Your problem statement has dots at the end and I am assumming that there is somemore left out, if you can completely jot down the problem, I may try to help you? – Satish Ramanathan Dec 15 '15 at 15:47
• No thats it! @satishramanathan – Bob Dec 15 '15 at 15:49
• @satishramanathan I really just need help on part B now, i've figured out everything else – Bob Dec 15 '15 at 15:59
• You wrote this very question before, then edited it in this way, asking for it to be removed. Why did you post it anew? – user228113 Dec 15 '15 at 16:51
• I edited the question to put the CI into proper math notation. It is a standard t-confidence interval. I did not add or remove dots. (b) Does the mean value for the US lie within the CI for the state in question? (c) CI gets shorter as $n$ gets larger. Beyond that it is difficult to know what kind of help you are looking for. – BruceET Dec 15 '15 at 23:11