Question

Kathy decides that she wants to know the 98 % confidence interval for a population mean despite originally setting out to find the 90 % confidence interval. How will this affect the width and the margin of error of her confidence interval for a population mean? Assume that the population standard deviation is unknown and the population distribution is approximately normal.

Select your answer from the choices below Answer
A. Keypad The width will decrease, and the margin of error will decrease.
B. The width will increase, and the margin of error will decrease
C. The width will decrease, and the margin of error will increase.
D. The width will increase, and the margin of error will increase.

Answer 1

Shifting from a 90% to a 98% confidence interval, the width and margin of error both increase, as a higher z-score is used to accommodate more certainty that the interval includes the true population mean. So the correct answer is option D.

Step-by-step explanation:

When Kathy decides to change from finding a 90% confidence interval for a population mean to a 98% confidence interval, assuming the population standard deviation is unknown and the population is approximately normal, this will affect the width and the margin of error of her confidence interval. An increase in the confidence level from 90% to 98% will cause an increase in the confidence interval width and also increase the margin of error.

This is because a higher confidence level means that we want to be more certain that our confidence interval contains the true population mean. This certainty is achieved by widening the interval. Mathematically, the margin of error depends on the z-score associated with the chosen confidence level and the standard error of the sample mean. The z-score for 98% confidence is higher than that for 90% confidence, leading to a larger margin of error and a wider interval.

Therefore, the correct answer is:
D. The width will increase, and the margin of error will increase.