# Confidence Intervals. Why Just One Sample?

#### TheStatProf

##### New Member
A typical problem in a Stat Textbook for creating a confidence Interval sounds like this: A sample of 50 blood pressures is taken and the sample has a mean of 120 with a standard deviation of 5. Construct a 95% confidence interval. What troubles me is that only one sample is enough. Intuitively, would it not be better to take numerous samples of size 50 and use the mean of the sample means, as well as the std dev of the sample means?

#### Sttepanka

##### New Member
Hi, why do you think one sample is enough?

#### hlsmith

##### Less is more. Stay pure. Stay poor.
Thestatprof,

Do you recall the written definition of the confidence interval?

#### ondansetron

##### TS Contributor
A typical problem in a Stat Textbook for creating a confidence Interval sounds like this: A sample of 50 blood pressures is taken and the sample has a mean of 120 with a standard deviation of 5. Construct a 95% confidence interval. What troubles me is that only one sample is enough. Intuitively, would it not be better to take numerous samples of size 50 and use the mean of the sample means, as well as the std dev of the sample means?
Ideally, we would just obtain the population data and we wouldn't need a CI, but we can't, and it's also not very practical to truly take repeated samples. The assumptions behind the interval generation (random, representative sample from an approximately normal distribution, or from a sample large enough to have a relatively normal sampling distribution, for example) allow us to benefit from good properties of the method. Additionally, you can use resampling techniques to simulate what you've described. The results can be quite accurate.