Question

You collect a random sample of size n from a population and calculate a 90% confidence interval. Which of the following strategies would produce a new confidence interval with an increased margin of error?

A. Use an 80% confidence level.

B. Use the same confidence level, but compute the interval n times. Approximately 10% of these intervals will be larger.

C. Use an 85% confidence level.

D. Decrease the sample size.

E. Nothing can guarantee that you will obtain a larger margin of error. You can only say that the chance of obtaining a larger interval is 0.10.

Answer 1

To increase the margin of error in a confidence interval with the same level of confidence, you would decrease the sample size, leading to a larger confidence interval.

Step-by-step explanation:

The question deals with how different choices can affect the margin of error in a confidence interval. If we want to increase the margin of error for a confidence interval with the same level of confidence, we would need to decrease the sample size. This is because a smaller sample size results in greater variability, which in turn leads to a larger margin of error and thus, a larger confidence interval to capture the true population mean. This is the answer corresponding to option D. Options A, B, and C suggest changes in the confidence level, which will change the width of the confidence interval but not necessarily guarantee an increased margin of error. Option E incorrectly suggests there's no certain way to increase the margin of error. To be clear, the margin of error is directly affected by sample size and confidence level.