Standard Error and Confidence Intervals Flashcards
What is standard error (SE)?
A measure of the variability of the sample mean from the true population mean.
How is standard error calculated?
O/sqr of n
σ is the population standard deviation and
n is the sample size.
What does a smaller standard error indicate?
Greater precision of the sample mean in estimating the population mean.
What is the relationship between standard deviation and standard error?
Standard deviation measures variability within a sample, while standard error measures variability across samples.
What is a confidence interval?
A range of values within which the population parameter is likely to fall with a given level of confidence (e.g., 95%).
What does increasing the confidence level do to the confidence interval?
A higher confidence level results in a wider confidence interval.
What factors influence the standard error?
Sample size – larger samples decrease SE.
Population variability – higher variability increases SE.
How do you calculate a confidence interval?
ˉ
X±Z×SE
Where:
ˉ
𝑋 = sample mean
Z = Z-score corresponding to confidence level
SE = standard error
What is the purpose of a confidence interval?
To estimate the uncertainty of a sample statistic and provide a range in which the true population parameter is expected to lie.
What happens to the confidence interval if the sample size increases?
The confidence interval becomes narrower, providing a more precise estimate.
What is the relationship between standard error and confidence intervals?
The standard error is used to calculate the margin of error in confidence intervals, affecting the interval width.
Why do we use standard error instead of standard deviation in confidence intervals?
Standard error accounts for sampling variability, while standard deviation measures variability within a sample.
