Interval Estimates of the Mean from Large Samples

What is an interval estimate of the mean from large samples?

An interval estimate of the mean from large samples is a range of values that is used to estimate the value of the population mean. The interval estimate is calculated using the sample mean, the sample standard deviation, and the confidence level.

How is an interval estimate of the mean from large samples calculated?

An interval estimate of the mean from large samples is calculated using the following formula:

confidence interval = sample mean ± z * (sample standard deviation / sqrt(n))

where:

• confidence interval is the range of values that is used to estimate the population mean
• sample mean is the mean of the sample data
• z is the z-score for the desired confidence level
• sample standard deviation is the standard deviation of the sample data
• n is the sample size

What is the importance of interval estimates of the mean from large samples?

Interval estimates of the mean from large samples are important because they can be used to make inferences about the population mean. For example, if we want to estimate the mean height of all adult males in the United States, we could take a sample of adult males and use the interval estimate to calculate a range of values that is likely to contain the true value of the population mean.

Multiple choice questions on interval estimates of the mean from large samples

Here are some multiple choice questions on interval estimates of the mean from large samples with answers:

1. Which of the following is not an interval estimate of the mean from large samples?
   • 95% confidence interval
   • 99% confidence interval
   • 90% prediction interval
   • All of the above are interval estimates of the mean from large samples.
   • The answer is 90% prediction interval. A prediction interval is used to estimate the value of a future observation, not the mean of the population.
2. How is an interval estimate of the mean from large samples calculated?
   • Using the sample mean, the sample standard deviation, and the confidence level.
   • By taking a sample of the population and then using that sample to make inferences about the population.
   • By asking experts to provide their opinions about the value.
   • All of the above.
   • The answer is Using the sample mean, the sample standard deviation, and the confidence level. Interval estimates of the mean from large samples can be calculated using a variety of methods, but this is the most common method.
3. What is the difference between a confidence interval and a prediction interval?
   • A confidence interval is used to estimate the value of an unknown population parameter. A prediction interval is used to estimate the value of a future observation.
   • A confidence interval is more accurate than a prediction interval.
   • A prediction interval is more precise than a confidence interval.
   • All of the above.
   • The answer is A confidence interval is used to estimate the value of an unknown population parameter. A prediction interval is used to estimate the value of a future observation. Confidence intervals are typically more accurate than prediction intervals, but they are less precise.