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The margin of error acts as a buffer from the sample parameter to account for the random sampling error that can occur when taking a sample from a population.
It determines the distance between the sample parameter and the upper & lower bounds of the confidence interval.
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)
CI = sample parameter ± MoE
CI = 23.2 ± 1.1
The larger our sample size... ➡️ The closer our sample hugs the true population mean (Central Limit Theorem)... ➡️ The narrower our confidence interval!
