A random sample has been taken from a normal distribution...

A random sample has been taken from a normal distribution and the following confidence intervals constructed using the same data: (37.53,49.87) and (35.59,51.81) (a) What is the value of the sample mean? (b) One of these intervals is a $99 \% \mathrm{CI}$ and the other is a $95 \%$ CI. Which one is the $95 \%$ CI and why?

A random sample has been taken from a normal distribution and the following confidence intervals constructed using the same data: (37.53,49.87) and (35.59,51.81)
(a) What is the value of the sample mean?
(b) One of these intervals is a $99 \% \mathrm{CI}$ and the other is a $95 \%$
CI. Which one is the $95 \%$ CI and why?

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Confidence Interval

A confidence interval is a range of values, derived from sample data, that is likely to contain the true value of an unknown population parameter. The interval is constructed using a confidence level, which represents the probability that the interval computed from a random sample includes the true parameter value.

Sample Mean

The sample mean is a statistical measure that represents the average value of a set of observations drawn from a population. In the context of a confidence interval, the sample mean is typically the central value of the interval, indicating that the interval is symmetrically built around this point.

Interval Width and Confidence Level Relationship

The width of a confidence interval is directly related to the confidence level and the variability in the data. A higher confidence level, such as 99%, requires a wider interval to ensure that it captures the true parameter with the stated level of certainty, whereas a lower confidence level, such as 95%, results in a narrower interval because it allows for a higher risk of not covering the true parameter.

Transcript

Please give Ace some feedback