What is the relationship between Sample Size and the width of the Confidence Interval? Please explain further as to why.
I understand the relationship, but I can't figure out the why
The measure of variability for distribution of means = SEm = SD/√n
Note that as n increases, SEm decreases.
Larger samples (n) are less likely to be biased one way or the other.
The relationship between sample size and the width of the confidence interval is inverse. As the sample size increases, the width of the confidence interval tends to decrease, and vice versa.
To understand why this happens, you need to know that the width of a confidence interval is influenced by two factors: the variability of the data and the desired level of confidence.
When you have a larger sample size, it provides more information about the population, resulting in a more precise estimate of the parameter you are trying to estimate (e.g., the mean, proportion, etc.). With more data, you can reduce the variability or spread of the sample data. As a result, the confidence interval tends to become narrower.
In simple terms, imagine you want to estimate the average height of a specific population. If you collect data from only a few individuals, there is a higher chance that your sample may not accurately represent the population, leading to a wider confidence interval. On the other hand, if you gather data from a large number of individuals, you are more likely to capture a better representation of the population's average height, resulting in a narrower confidence interval.
To summarize, increasing the sample size reduces the uncertainty in your estimate, leading to a narrower confidence interval. This is because more data provides more information and improves the precision of your estimate, decreasing the spread of possible values around the estimated parameter.