A total of 300 observations of Bob Ramos, an assembly-line worker, were made ove

Question

A total of 300 observations of Bob Ramos, an assembly-line worker, were made over a 40-hour work week. The sample also showed that Bob was busy working (assembling the parts) during 240 observations. (Round all intermediate calculations to at least two decimal places before proceeding with further calculations.) a) The percent of time Bob is working- 80 % (enter your response as a percentage rounded to two decimal placed). b) The number of observations that need to be taken of Bob to be 95% confident with 4% acceptable error-D round your response to the immediate higher whole number).

Explanation / Answer

To be calculated:

a) Efficiency of Bob

b) Number of observations required or sample size (95% confidence, 4% acceptable error)

c) If the sample size is adequate or not

Given Values:

Sample size, S = 300

Sample size where Bob was found to be working = 240

Solution:

a) Percent of time Bob is working can be calculated as;

Efficiency = ( Number of samples Bob was working / Total number of samples ) x 100

Efficiency = ( 240 / 300 ) x 100 = 0.80 x 100

Efficiency = 80%

b) Sample size can be calculated as;

S = [(Z^2) x P x (1 - P)] / (C^2)

where, z = z value, p = percentage picking a choice, c = confidence interval

Z (at 95% confidence) = 1.96, P = 0.80, C (at 4% acceptable error) = 4 / 100 = 0.04

Therefore, S = [(1.96^2) x (0.80) x (0.20)] / (0.04^2)

S = 0.615 / 0.0016

S = 384.37

S = 384

The number of observations that need to be taken of Bob to be 95% confident with 4% acceptable error is 384 samples.

c) The current number of observations of Bob Ramos are 300, while the required number of observations are 384. Therefore, the current sample size is not adequate as it is little less than the required sample size.

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