According to a recent survey, the mean income before taxes of consumer units (i. e., households) in the U. S. was $60,533 with a margin of error equal to 1406.32 (for a 95% confidence level). Calculate a 95% confidence level for the population mean income before taxes for all U. S. consumer units. A (58,681.82, 62,384.18) B (57,776.61, 63,289.39) C (59,097.98, 61,968.02) D (59,126.68, 61,939.32) E (60,166.92, 60,899.08)

Question

Mathematics

Jaden Weeks

27 June, 22:52

According to a recent survey, the mean income before taxes of consumer units (i. e., households) in the U. S. was $60,533 with a margin of error equal to 1406.32 (for a 95% confidence level). Calculate a 95% confidence level for the population mean income before taxes for all U. S. consumer units. A (58,681.82, 62,384.18) B (57,776.61, 63,289.39) C (59,097.98, 61,968.02) D (59,126.68, 61,939.32) E (60,166.92, 60,899.08)

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Tessa · Answer 1

D (59,126.68, 61,939.32)

Step-by-step explanation:

A confidence interval has two bounds, a lower bound and an upper bound. These bounds depend of the sample mean and of the margin of error.

The lower bound is the sample mean subtracted by the margin of error.

The upper bound is the margin of error added to the sample mean.

In this question:

Sample mean: 60,533

Margin of error: 1406.32

Lower bound: 60,533 - 1406.32 = 59,126.28

Upper bound: 60,533 + 1406.32 = 61,939.32

So the correct answer is:

D (59,126.68, 61,939.32)