Each year, Lord & Taylor, Ltd., sets up a gift-wrapping station to assist its cu

Question

Each year, Lord & Taylor, Ltd., sets up a gift-wrapping station to assist its customers with holiday shopping. Preliminary observations of one worker at the station produced the following sample time (in minutes per package): 3.5, 3.3, 4.1, 3.5, 4.0. Assume a 99% confidence level and an accuracy of 5%. (Round all intermediate calculations to two decimal places before proceeding with further calculations.)

Based on this small sample and the given confidence level and accuracy level, the number of observations that would be necessary to determine the true cycle time = __ observations.

Explanation / Answer

Sample = 3.5,3.3,4.1,3.5,4.0

mean = 3.68

S.D = (.488/4)1/2 = .3492

Z= 2.58 at 99% confidence level

accuracy level = h = .05

sample size= (zs/hx)2

= ((2.58*0.3492)/(.05*3.68))2

= (.900936/.184)2

= 23.97

= 24 observations

Values x-mean (x-mean)^2 (x-mean)^2 3.5 3.5-3.68 (3.5-3.68)^2 0.0324 3.3 3.3-3.68 (3.3-3.68)^2 0.1444 4.1 4.1-3.68 (4.1-3.68)^2 0.1764 3.5 3.5-3.68 (3.5-3.68)^2 0.0324 4 4-3.68 (4-3.68)^2 0.1024

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