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Imagine you're trying to estimate the percentage of air passengers who prefer aisle seats. You want a window around your estimate that tells you how confident you are in this guess. That's called a confidence interval.
A confidence interval gives you a range of values that you're fairly sure the true population parameter (e.g., the actual percentage of all passengers who prefer aisle seats) lies within.
For instance, if you say you're 95% confident that the true percentage of passengers preferring aisle seats is between 35% and 45%, your confidence interval is 35% to 45%. The 95% confidence level means that if you were to take 100 different samples and compute a confidence interval for each, we'd expect about 95 of them to contain the true population parameter.

When you conduct a survey, your results might not be exactly pinpoint accurate. The margin of error helps you understand how far off your sample results might be from the true population value.
The margin of error is typically expressed as a percentage and gives you the radius of the range. It tells you how much you can expect your survey results to differ from the actual population percentage. For example, if your survey says 50% of passengers prefer aisle seats and your margin of error is 2.5%, then you believe the true percentage is between 47.5% and 52.5%.
The margin of error becomes smaller when you have a larger sample size. So, if you want more precise results, you need to survey more people.

The population proportion is the fraction of the entire population that has a particular attribute of interest. For example, in your survey, it's the proportion of all air passengers who prefer aisle seats. Let’s denote population proportion by the symbol p.
If you don't know this value, you can sometimes use 0.5 (maximum variability), but it's better to use a prior survey result if available. In our exercise, previous data suggests 38% of passengers prefer aisle seats, so p = 0.38.
Using a correct population proportion helps provide accurate sample size calculations and confidence intervals, ensuring your data collection is effective and meaningful.

The Z-score tells you how many standard deviations an element is from the mean. In sample size calculations for confidence intervals, it reflects how confident you want to be that your interval captures the true population parameter.
Common Z-scores are:

• 1.645 for 90% confidence
• 1.96 for 95% confidence
• 2.576 for 99% confidence

For a 95% confidence level, our Z-score is 1.96.
Essentially, a higher Z-score means you're more certain about your estimate, but it also means you'll need a larger sample to achieve that level of certainty. So, there's a balance between being confident in your results and the effort required to gather data.