SOLUTION: 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

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Question 1203978: 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:

Summary
Groups Sample Size Sum Average Variance
Line A 6 250 41.66667 0.266667
Line B 6 260 43.33333 0.666667
Line C 6 249 41.5 0.7

ANOVA
Source of Variation SS df MS F p-value
Between Groups 12.33333 2 6.166667 11.32653 0.001005
Within Groups 8.166667 15 0.544444
Total 20.5 17
Compute 99% confidence intervals that estimate the difference between each pair of means. (Negative amount should be indicated by a minus sign. Round your answers to 2 decimal places.) Which pairs of means are statistically different?
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
i found a calculator online at https://statpages.info/anova1sm.htmlthat does the analysis you are looking for.
it works off the mean and the standard deviation, i.e. uses summarized data.
i used the summarized data you had and got similar results.
this indicates to me that the results were consistent with what you got.
it also does the sample to sample posthoc analysis.
the results as shown below.

group 1 was line A
group 2 was line B
group 3 was line C.

the results indicate that line A to line B are statistically different from each other because the p-value was .0037 which is less than .01.

standard deviation = square root of variance, so i took the square root of the variance given and used that as input to the calculator.
i round to 6 decimal digits which is usually enough for accurate readings.