Question

question 6 of 10
which confidence level would produce the widest interval when estimating
the mean of a population based on the mean and standard deviation of a
sample of that population?

a. 83%

b. 57%

c. 42%

d. 69%

Explanation:

Step1: Recall Confidence Interval Concept

A confidence interval for a population mean (when using sample mean and standard deviation) has a margin of error related to the confidence level. Higher confidence levels correspond to larger critical values (e.g., z - value or t - value), which increase the margin of error and thus widen the interval.

Step2: Compare Confidence Levels

Among the given options (83%, 57%, 42%, 69%), 83% is the highest confidence level. A higher confidence level means we want to be more certain that the population mean lies within the interval, so we use a larger critical value, leading to a wider interval.

To determine which confidence level produces the widest interval for estimating a population mean, we use the concept that higher confidence levels correspond to larger critical values (e.g., z - or t - values). Larger critical values increase the margin of error, which widens the confidence interval. Among the options (83%, 57%, 42%, 69%), 83% is the highest confidence level, so it will produce the widest interval.

Answer:

A. 83%