What are confidence intervals?
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A confidence interval enables one to obtain a range of values in which the true population parameter lies, with a defined confidence level.
Scenario: At Crammer Nation University, Sigma Apple Pi brothers claim to get a lot of Tinder matches. You take a random sample of 35 brothers and find a sample mean of 23.2 daily Tinder matches per brother with a standard deviation of 3.2 matches. Based on this, find a 95% confidence interval for the true mean daily Tinder matches of Sigma Apple Pi brothers.
CI = (22.1, 24.3)
Answer: This means we're 95% confident that the true mean Tinder matches per day for brothers of Sigma Apple Pie lies between 22.1 and 24.3 for the entire population of brothers in the chapter.
In the above scenario, our sampling distribution would resemble a t-distribution like so:
We are not saying that there's a 95% probability... rather that we are 95% confident that the true population parameter lies within these bounds.