What is an interval estimate?
An interval estimate is a range of values that is used to estimate the value of an unknown population parameter. 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 mean height of the sample to calculate an interval estimate for the population mean. The interval estimate would be a range of values that is likely to contain the true value of the population mean.
How are interval estimates calculated?
Interval estimates are calculated using a variety of methods, including:
- The confidence interval
- The prediction interval
- The tolerance interval
The confidence interval
The confidence interval is the most common type of interval estimate. It is calculated by taking the sample mean and adding and subtracting a margin of error. The margin of error is calculated using the sample standard deviation and the desired confidence level.
For example, if we want to calculate a 95% confidence interval for the mean height of all adult males in the United States, we would first calculate the sample mean. Then, we would calculate the sample standard deviation. Finally, we would multiply the sample standard deviation by 1.96 (the z-score for a 95% confidence level) and add and subtract that value from the sample mean. The resulting range of values would be a 95% confidence interval for the population mean.
The prediction interval
The prediction interval is similar to the confidence interval, but it is used to estimate the value of a future observation. The prediction interval is calculated by taking the sample mean and adding and subtracting a margin of prediction error. The margin of prediction error is calculated using the sample standard deviation, the desired confidence level, and the number of future observations.
The tolerance interval
The tolerance interval is used to estimate the range of values that will contain a certain percentage of the population. The tolerance interval is calculated by taking the sample mean and adding and subtracting a margin of tolerance. The margin of tolerance is calculated using the sample standard deviation, the desired confidence level, and the desired percentage of the population.
The importance of interval estimates
Interval estimates are an important tool for making inferences about populations from samples. They can be used to estimate the mean, median, standard deviation, and other population parameters. Interval estimates are also used in hypothesis testing and decision making.
Multiple choice questions on interval estimates and confidence intervals
Here are some multiple choice questions on interval estimates and confidence intervals with answers:
- Which of the following is not an interval estimate?
- Confidence interval
- Prediction interval
- Tolerance interval
- All of the above are interval estimates.
- The answer is All of the above are interval estimates.
- How are interval estimates calculated?
- Using the sample mean, the sample standard deviation, and the desired 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 desired confidence level. Interval estimates can be calculated using a variety of methods, depending on the type of data and the desired level of accuracy.
- 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.