Hoping to lure more shoppers downtown, a city builds a new public parking garage

Question

Hoping to lure more shoppers downtown, a city builds a new public parking garage in the central business district. The city plans to pay for the structure through parking fees. For a two-month period (43 weekdays), daily fees collected averaged $1,262 with a standard deviation of $170. The 95% confidence interval for the mean daily income is $1,210 to $1,314.

(d) How many days' worth of data must planners collect to have 99% confidence of estimating the true mean to within $10? (Use a z-interval to simplify the calculations.)

Planners must collect __ days' worth of data.

z P(Z less than or equal to negative z) 0.6745 0.25 0.7063 0.24 0.7388 0.23 0.7722 0.22 0.8064 0.21 0.8416 0.2 0.8779 0.19 0.9154 0.18 0.9542 0.17 0.9945 0.16 1.0364 0.15 1.0803 0.14 1.1264 0.13 1.175 0.12 1.2265 0.11 1.2816 0.1 1.3408 0.09 1.4051 0.08 1.4758 0.07 1.5548 0.06 1.6449 0.05 1.7507 0.04 1.8808 0.03 1.96 0.025 2.0537 0.02 2.1701 0.015 2.3263 0.01 2.5758 0.005 2.807 0.0025 3.0902 0.001 3.2905 0.0005 3.719 0.0001 3.8906 0.00005 4.2649 0.00001 4.4172 0.000005

Explanation / Answer

Planners must collect 1918 days' worth of data

for 99 % CI value of z= 2.5758 standard deviation = 170 margin of error E = 10 required sample size n=(z/E)2                                         = 1918

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