ABET Outcome Performae Criteria: b2- Use statistical methods to an (b) A work sa

Question

ABET Outcome Performae Criteria: b2- Use statistical methods to an (b) A work sampling analyst notices that out of 50 observations, a worker is taking a k 2 times, chatting to a co-worker 2 times, and is absent from the workstation once. The analyst is 95% confident that the worker is actually working from is 95% confident that the worker is working from 87% to 93% of the time, what changes have occurred in the work sampling study? brea %to % of the time. If the statement is changed to: the analyst

Explanation / Answer

(a)

The sample size is determined by the following formula:

[n=(rac{z}{e})^{2}.p(1-p)]

or,

[e=sqrt{rac{z^{2}.p(1-p)}{n}}]

Where

z = standard normal variable at /2 = NORM.INV(1-(1-0.95)/2,0,1) = 1.96
n = sample size = 50
p = sample proportion = (4+2+2)/50 = 16%

So, e = sqrt(1.96*1.96*0.16*(1-0.16)/50) = 0.10

So, with 95% of confidence level, the idle time is between (16% - 10%) and (16% + 10%) i.e. 6% to 26%

So, with 95% of confidence level, the working time is between 74% to 94%

(b)

Note that the range is still 20% (= 98% - 78%) this means that 'e' haven't changed.

z is also the same as the confidence level is 95%.

This means p must have changed (reduced from 16% to 12%).

This means the 50 observations have shown idle time of 50*12% = 6 times

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