An organization advocating for healthcare reform has estimated the average cost of providing healthcare for a senior citizen receiving Medicare to be about $13,000 per year. The article also stated that, with 90% confidence, the margin or error for the estimate is $1,000. Determine the resulting 90% confidence interval for the average cost for healthcare of a senior citizen receiving Medicare.

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02-12-2021
Mathematics

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An organization advocating for healthcare reform has estimated the average cost of providing healthcare for a senior citizen receiving Medicare to be about $13,000 per year. The article also stated that, with 90% confidence, the margin or error for the estimate is $1,000. Determine the resulting 90% confidence interval for the average cost for healthcare of a senior citizen receiving Medicare.

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Joaobezerraidn Joaobezerraidn · Answer 1 · 2021-12-10T05:23:29-05:00

Using the definition of a confidence interval, it is found that the 90% confidence interval for the average cost for healthcare of a senior citizen receiving Medicare is ($12,000, $14,000).

A confidence interval is the sample mean plus/minus the margin of error.

In this problem, the sample mean is of $13,000.

The margin of error is of $1,000.

Hence:

$13,000 - $1,000 = $13,000

$13,000 + $1,000 = $14,000

The interval is ($12,000, $14,000).

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