Question

The operations manager of a large production plant would like to estimate the average amount of time workers take to assemble a new electronic component. After observing a number of workers assembling similar devices, she estimates that the standard deviation is 0.25 hour. How large a sample of workers should she select if she wishes to estimate the mean assembly time to within 3.2 minutes at the 98% confidence level?

Answer 1

Solution:

Given:

Standard deviation = hour

E = Margin of Error = 3.2 minutes

Since Standard deviation is in hour and Margin of Error is in minutes, we need to convert both in same units.

Multiply standard deviation by 60 minutes to convert it in minutes.

Thus we get:

Standard deviation = minutes

that is: minutes

c = confidence level = 98%

Formula:

Z_c is z critical value for c = 0.98 confidence level.

Find Area = ( 1+c)/2 = ( 1 + 0.98 ) / 2 = 1.98 /2 = 0.9900

Thus look in z table for Area = 0.9900 or its closest area and find corresponding z critical value.

Area 0.9901 is closest to 0.9900 , thus corresponding z value is 2.3 and 0.03

Thus Z_c = 2.33

Thus

( Sample size is always rounded up).