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? Use an 80% confidence level. Use the same confidence level, but compute the interval n times. Approximately 10% of these intervals will be larger. Use an 85% confidence level. Decrease the sample size. 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.

Question

Mathematics

Chanel Campbell

31 January, 01:41

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? Use an 80% confidence level. Use the same confidence level, but compute the interval n times. Approximately 10% of these intervals will be larger. Use an 85% confidence level. Decrease the sample size. 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.

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Answers (1)

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Dayton Salazar · Answer 1

Decrease the sample size.

Step-by-step explanation:

Margin of error is:

ME = CV * √ (σ / n)

where σ is the population standard deviation, or:

ME = CV * √ (p (1 - p) / n)

where p is the proportion.

In each case, the margin of error is directly proportional to the critical value, and inversely proportional to √n.

Lowering the confidence level will lower the critical value, which will decrease the margin of error. Decreasing the sample size will increase the margin of error.