Which of the following occurs if a 90% confidence interval increases to 95%?

A confidence interval provides a range within which we expect a population parameter to lie, based on sample data. Increasing the confidence level means we want to be more certain that the interval contains the parameter, which affects the margin of error.

Option A:The margin of error does not change.

Rationale:This is incorrect. Increasing the confidence level requires a wider interval to maintain the higher degree of certainty, which increases the margin of error.

Option B:The interval remains the same.

Rationale:This is incorrect. To achieve a higher confidence level, the interval must widen, altering its range.

Option C:The interval becomes narrower.

Rationale:This is incorrect. A higher confidence level necessitates a wider interval to ensure the parameter is captured within the range.

Option D:The margin of error increases.

Rationale:Correct. Increasing the confidence level from 90% to 95% means we are more confident that the interval contains the true parameter. To achieve this increased confidence, the margin of error must increase, resulting in a wider interval.