Three assembly lines are used to produce a certain component

Three assembly lines are used to produce a certain component for an airliner. To examine the production rate, a random sample of six hourly periods is chosen for each assembly line and the number of components produced during these periods for each line is recorded. The output from a statistical software package is:

Solution

We may use the following formula for confidence limits.
(mean B - mean C) +/- t sqrt(MSW(1/6+1/6))
t is the t-value 2.947 with 15 degrees of freedom
(43.33333-41.5) +/- 2.947 sqrt(0.544444*2/6)
1.83333+/- (2.947)
1.83333+/- (2.947) 0.42600626
1.8333+/-1.2554
The above 2 values are the 99 % confidence limits