Hi, I’m so confused about the sample size when we refer to the term confidence interval

In this slide, sample size n = 1, I understand that to get the right plot we just need to take more samples, right? (because n=1, so mean of the sample is the value of this sample)

In case, sample size n = 10, does it mean, in each line, the blue dot is the mean of 10 samples? Therefore, if we need many lines as in the image, for example 20 lines, then we need to take 200 samples (10 for each line). Is it correct?

Thank you for your help!

Hi @hiddenpieces. Yes, each blue dot in that image would be the mean of the sample which is just the single sample value, since n = 1. The horizontal bars around each blue dot are the confidence intervals for each sample. For sample size n = 1, the standard deviation is 0, so each bar on the plot would be the same size.

When you have a sample size of n = 10 as you mentioned, the blue dot in the center of that sample’s confidence interval can be seen as the mean of all n values. However, do note that the confidence intervals can appear differently than what’s shown in the image because they depend on the data’s standard deviation.

Also, if you create larger sample sizes, you might start to see the means get closer to the population mean. For instance, if you took a single sample of size 200 and drew the confidence interval for that, the mean would be fairly close to the population mean \mu. When the sample sizes are larger you might not see as many red lines that don’t overlap the population mean.

Hope this helps!

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