If the population variance is increased and other factors are the same, the width of a confidence interval for the population mean tends to increase.

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Quizplus · Accepted Answer

When the population variance is increased, the standard error of the mean also increases, which leads to a wider confidence interval for the population mean. This can be seen from the formula for the margin of error: ME = z* (sigma/sqrt(n)), where sigma is the population standard deviation (which is proportional to the square root of the variance) and n is the sample size. If sigma increases, the margin of error and hence the confidence interval width also increase.

If the Population Variance Is Increased and Other Factors Are