Question

Alarge population of measurements has unknown mean and standard deviation. Two different random samples of 50 measurements are thken from the population. A 95 s. confidence interval for the population mean is constructed for each sample. Which statement would most likely be true of these two confidence intictrats:

A. They would have the same margin of error
B. The confidence interval's would have the same cemer but different widshis
C. They would have identical values for the lower and upper limits of the confidence interval
D. None of the above is true

Answer 1

The correct statement about the two confidence intervals for the population mean is that they would have the same center but different widths.

Step-by-step explanation:

The correct statement about the two confidence intervals for the population mean is B. The confidence intervals would have the same center but different widths.

When constructing a confidence interval for the population mean, the center of the interval is the sample mean for both samples. However, the width of the confidence interval depends on the sample standard deviation and the sample size. Since the two samples are different, their standard deviations may vary, resulting in different widths for the confidence intervals.