What are some examples of confidence intervals?

What are some examples of confidence intervals?

Confidence intervals are used in statistics to estimate the range within which a population parameter lies. For example, if a survey shows that 60% of people prefer product A over product B, a 95% confidence interval might be 55% to 65%. This means we can be 95% confident that the true preference in the population falls within this range.

Can you give me another example?

Sure! Let's say a researcher measures the average height of a sample of 100 adult men and finds it to be 175 cm. If the 95% confidence interval is calculated to be 172 cm to 178 cm, it suggests that the average height of all adult men in the population is likely between 172 cm and 178 cm.

How do you calculate a confidence interval?

To calculate a confidence interval, you typically need the sample mean, the standard deviation, and the sample size. The formula is:

Confidence Interval = Sample Mean ± (Z-score * (Standard Deviation / √Sample Size))

The Z-score corresponds to the desired confidence level (e.g., 1.96 for 95% confidence).

What does a wider confidence interval indicate?

A wider confidence interval indicates more uncertainty about the estimate of the population parameter. It suggests that the sample data is more variable or that the sample size is smaller, leading to less precision in the estimate.