Asked by Kaparya White on Jun 25, 2024
Verified
When the variance of the mean value is smaller than the variance of individual values,________.
A) the p-value is equal to the Significance F
B) the data set contains an outlier
C) the Adjusted R Square is equal to 1
D) the prediction interval is wider than the confidence interval
Variance
The square of the standard deviation, indicating how much the values in a set vary from the mean.
Prediction Interval
A range of values that is likely to contain the value of an unknown parameter for a given level of confidence.
Confidence Interval
A range of values, derived from sample data, that is likely to contain the value of an unknown population parameter with a specified level of confidence.
- Comprehend the significance of variance in mean value, prediction, and confidence intervals.
Verified Answer
SL
Samantha LópezJun 29, 2024
Final Answer :
D
Explanation :
When the variance of the mean value is smaller than the variance of individual values, it indicates that the mean provides a more precise estimate of the population parameter than individual observations do. This situation typically results in a narrower confidence interval for the mean estimate compared to the prediction interval for individual observations, as the prediction interval accounts for the additional variability of individual values around the mean.
Learning Objectives
- Comprehend the significance of variance in mean value, prediction, and confidence intervals.