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) ?

Question

Mathematics

Porter Benjamin

8 March, 22:58

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) ?

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Tony Clements · Answer 1

Mean time is 22.4 hours

Step-by-step explanation:

Sample size is 40

Standard deviation is σ = 9 hours

For 95% confidence interval z*=1.96 from z * value tables

The formula to apply here is z = (x-μ) / δ where;

z=z * score value = 1.96

x=sample size=40

μ=mean time taken

δ=population standard deviation=9

z = (x-μ) / δ

1.96 = (40-μ) / 9

1.96*9=40-μ

17.64=40-μ

μ=40-17.64

μ=22.36

μ=22.4