Question

Exercise 8.9 (Algorithmic)} 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 WEBfile 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 = 12 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? Round your answer to one decimal place. to hours

Return Preparation Time(Hours)
35.3
30.5
37.4
26.5
13.0
49.9
28.8
44.0
61.6
0.5
40.5
34.9
47.9
36.6
24.1
39.8
47.8
18.5
36.6
39.2
14.5
37.3
40.5
49.3
45.5
28.3
19.5
5.6
52.6
41.4
45.3
39.0
33.7
29.4
14.5
40.1
33.7
36.9
5.6
33.7

Answer 1

sample mean, xbar = 33.495
population standard deviation, σ = 12
sample size, n = 40

Given CI level is 95%, hence α = 1 - 0.95 = 0.05
α/2 = 0.05/2 = 0.025, Zc = Z(α/2) = 1.96

CI = (33.495 - 1.96 * 12/sqrt(40) , 33.495 + 1.96 * 12/sqrt(40))
CI = (29.8 , 37.2)