If we take samples from normal populations and construct two confidence intervals (CI) for which the only difference is that one of them was at the 80% confidence level and the other was at the 90% level, which of the following statements is true? Group of answer choices The margin of error is larger in the 90% CI than in the 80% CI. The margin of error is the same in the 90% CI as it is in the 80% CI. The margin of error is smaller in the 90% CI than in the 80% CI. There is not enough information to determine which of the above statements is true.

Question

Mathematics

Mathias Wang

18 December, 11:30

If we take samples from normal populations and construct two confidence intervals (CI) for which the only difference is that one of them was at the 80% confidence level and the other was at the 90% level, which of the following statements is true? Group of answer choices The margin of error is larger in the 90% CI than in the 80% CI. The margin of error is the same in the 90% CI as it is in the 80% CI. The margin of error is smaller in the 90% CI than in the 80% CI. There is not enough information to determine which of the above statements is true.

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Troy Henderson · Answer 1

Answer: The margin of error is larger in the 90% CI than in the 80% CI.

Step-by-step explanation:

Confidence interval is written as

Sample mean ± margin of error

Margin of error = z * population standard deviation/number of samples

The z score for a 90% confidence level (1.645) is higher than the z score for a 80% confidence level (1.282)

If all other parameters (sample size and population standard deviation) remain the same, then the true statement is

The margin of error is larger in the 90% CI than in the 80% CI.