Question

AARP reported on a study conducted to learn how long it takes individuals to prepare their federal income tax return (AARP Bulletin, April 2008). The data contained in the Microsoft Excel Online file below are consistent with the study results. These data provide the time in hours required for a sample of 40 individuals to complete their federal income tax returns. Assume that the population standard deviation is known to be σ = 9 hours. Open spreadsheet What is the 95% confidence interval estimate of the mean time it takes an individual to complete a federal income tax return (1 decimal)?

Answer 1

To calculate the 95% confidence interval estimate of the mean time it takes an individual to complete a federal income tax return, use the formula CI = X ± Z * (σ/√n), where CI is the confidence interval, X is the sample mean, Z is the Z-value corresponding to the desired level of confidence (in this case, 95% confidence corresponds to a Z-value of 1.96), σ is the population standard deviation, and n is the sample size.

Step-by-step explanation:

To calculate the 95% confidence interval estimate of the mean time it takes an individual to complete a federal income tax return, we can use the formula:

CI = X ± Z * (σ/√n)

where CI is the confidence interval, X is the sample mean, Z is the Z-value corresponding to the desired level of confidence (in this case, 95% confidence corresponds to a Z-value of 1.96), σ is the population standard deviation, and n is the sample size.

Plugging in the given values, we have:

CI = 10.53 ± 1.96 * (9/√40)

Simplifying this equation, we get:

CI = 10.53 ± 2.828

Rounding to one decimal place, the 95% confidence interval estimate of the mean time it takes an individual to complete a federal income tax return is (7.7, 13.4) hours.