A time study of a factory worker has revealed an average observed time of 3.40 m

Question

A time study of a factory worker has revealed an average observed time of 3.40 minutes, with a standard deviation of 1.65 minutes

These figures were based on a sample of 45 observations. Assume that the firm wants to be 95% confident that the standard time is within 55 % of the true value. (Round all intermediate calculations to two decimal places before proceeding with further calculations.)

Based on the given information and the given confidence level and accuracy level, the number of observations that would be necessary for the time study = ___ observations (round your response up to the next whole number).

Explanation / Answer

To be calculated:

Number of observations (n)

Given values:

Average observed time, x-bar = 3.40 minutes

Standard deviation in average observed time, S = 1.65 minutes

Number of observations in current sample = 45

Confidence level = 95%

Desired accuracy level, a = 55% or 0.55

Solution:

Number of observations is calculated using the below formula:

Number of observations, n = [ (Z / a) x (S / x-bar) ] ^ 2

where,

Z = Statistical confidence level

a = Desired accuracy level

S = Standard deviation in observed time

x-bar = Average observed time

From z-table, at 95% confidence level, Z = 1.96

Putting all the given values in the above formula, we get;

n = [ (Z / a) x (S / x-bar) ] ^ 2

n = [ (1.96 / 0.55) x (1.65 / 3.40) ] ^ 2

n = [ (3.56) x (0.49) ] ^ 2

n = (1.73) ^ 2

n = 2.99

n = 3 (rounding up to the next whole number)

The number of observations that would be necessary for the time study = 3 observations

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