AARP reported on a study conducted to learn howlong it takes individuals to prepare their federal income tax return (AARP Bulletin, April 2008). The data contained in the file named TaxReturn are consistent with the study results. These data provide the time in hours required for 40 individuals to complete their federal income tax returns. Using past years' data, the population standard deviation can be assumed known with σ = 9 hours.
Click on the webfile logo to reference the data. What is the 95% confidence interval estimate of the mean time it takes an individual to complete a federal income tax return (to 1 decimal)?
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:
Confidence Interval = Sample Mean ± (Critical Value) * (Standard Deviation / √(Sample Size))
Given that the population standard deviation is known (σ = 9 hours), we can find the critical value for a 95% confidence level using a standard normal distribution table or a statistical calculator. The critical value for a 95% confidence level is approximately 1.96.
Since the data is not provided and can only be accessed through a webfile, I am unable to directly calculate the sample mean and sample size. However, assuming you have access to the data, you can follow these steps to calculate the confidence interval:
1. Calculate the sample mean of the data.
2. Determine the sample size (number of individuals) in the data.
3. Calculate the standard deviation of the sample, which is the known population standard deviation (σ = 9 hours) divided by the square root of the sample size (√n).
4. Multiply the critical value (1.96 for 95% confidence level) by the standard deviation calculated in step 3.
5. Add and subtract the result from step 4 to the sample mean calculated in step 1 to get the lower and upper bounds of the confidence interval.
The final result will be a range of values representing the 95% confidence interval estimate of the mean time it takes an individual to complete a federal income tax return.