Asked by Claudia Riano on May 02, 2024
Verified
The width of the confidence interval estimate for the predicted value of y depends on
A) the standard error of the estimate
B) the value of x for which the prediction is being made
C) the sample size
D) All of these choices are true.
Confidence Interval Estimate
A spectrum of values, drawn from sample statistics, projected to embrace the value of an undefined population measure.
Standard Error
A statistical measure that quantifies the variability or dispersion of a sample statistic from the population parameter.
Sample Size
The number of observations or units chosen from a population to participate in a statistical study, influencing the study's validity and conclusions.
- Understand the impact of sample size, standard error, and x value on the width of confidence intervals.
Verified Answer
A) The standard error of the estimate: As the standard error of the estimate increases, the width of the confidence interval also increases, indicating less precision in the prediction.
B) The value of x for which the prediction is being made: The width of the confidence interval increases as x moves away from the mean of x, indicating that the prediction is less precise for extreme values of x.
C) The sample size: As the sample size increases, the standard error of the estimate decreases, leading to a narrower confidence interval and increased precision in the prediction.
Therefore, all three factors influence the width of the confidence interval estimate for the predicted value of y, and the correct answer is D.
Learning Objectives
- Understand the impact of sample size, standard error, and x value on the width of confidence intervals.
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