Question

Below are three 95% CIs (where 𝜎 was known and 𝑥̅happened to be the same); one with sample size 30, one with samplesize 40, and one with sample size 50. Which is which?(66.2, 76.2)(61.2, 81.2)(56.2, 86.2)

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Birdie

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To determine which confidence interval (CI) corresponds to each sample size, we need to compare the widths of the intervals.

The width of a confidence interval is determined by the sample size and the level of confidence.

Generally, the larger the sample size, the narrower the confidence interval.

Therefore, the CI with the narrowest width corresponds to the largest sample size, the CI with the widest width corresponds to the smallest sample size, and the CI of intermediate width corresponds to the remaining sample size.

Let's compare the widths of the given CIs.

For the CI (66.2, 76.2):

Width = upper limit - lower limit = 76.2 - 66.2 = 10

For the CI (61.2, 81.2):

Width = upper limit - lower limit = 81.2 - 61.2 = 20

For the CI (56.2, 86.2):

Width = upper limit - lower limit = 86.2 - 56.2 = 30

Comparing the widths, we can conclude that the CI (66.2, 76.2) corresponds to the largest sample size, the CI (61.2, 81.2) corresponds to the intermediate sample size, and the CI (56.2, 86.2) corresponds to the smallest sample size.

Answer: The CI (66.2, 76.2) corresponds to the sample size of 50, the CI (61.2, 81.2) corresponds to the sample size of 40, and the CI (56.2, 86.2) corresponds to the sample size of 30.

The width of a confidence interval is determined by the sample size and the level of confidence.

Generally, the larger the sample size, the narrower the confidence interval.

Therefore, the CI with the narrowest width corresponds to the largest sample size, the CI with the widest width corresponds to the smallest sample size, and the CI of intermediate width corresponds to the remaining sample size.

Let's compare the widths of the given CIs.

For the CI (66.2, 76.2):

Width = upper limit - lower limit = 76.2 - 66.2 = 10

For the CI (61.2, 81.2):

Width = upper limit - lower limit = 81.2 - 61.2 = 20

For the CI (56.2, 86.2):

Width = upper limit - lower limit = 86.2 - 56.2 = 30

Comparing the widths, we can conclude that the CI (66.2, 76.2) corresponds to the largest sample size, the CI (61.2, 81.2) corresponds to the intermediate sample size, and the CI (56.2, 86.2) corresponds to the smallest sample size.

Answer: The CI (66.2, 76.2) corresponds to the sample size of 50, the CI (61.2, 81.2) corresponds to the sample size of 40, and the CI (56.2, 86.2) corresponds to the sample size of 30.

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