Asked by Alejandro Otón García on Jun 03, 2024

verifed

Verified

Assuming the sample mean and standard deviation are the same for different combinations of levels of confidence and sample size, as the sample size ______, the level of confidence has ______ impact on the width of the confidence interval.

A) decreases; the same
B) decreases; less
C) increases; more
D) increases; less

Sample Size

The number of observations or data points collected in a sample from a population for the purpose of statistical analysis.

Confidence Interval

A range of values, derived from sample data, that likely contain the population parameter with a certain level of confidence.

Level of Confidence

The degree of certainty or probability that the results of statistical analysis are reliable and not due to random chance.

  • Examine how changes in sample size influence the width of a confidence interval.
  • Fathom the interrelation between confidence level and the finesse in confidence interval delineation.
verifed

Verified Answer

ZK
Zybrea KnightJun 06, 2024
Final Answer :
D
Explanation :
As the sample size increases, the impact of the level of confidence on the width of the confidence interval decreases because the standard error (which is part of the calculation for the confidence interval and depends on the sample size) becomes smaller, making changes in the z* or t* multiplier (which adjust for confidence level) less impactful on the overall width of the confidence interval.