HardStatistics & Data ScienceHigh School (9–10)High School (11–12)UndergraduateGeneralStatistics Basics › Learning from SamplesStatistics Basics › Probability and ChanceNumericalapplication
A workshop tests a new layout of its benches…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
A workshop tests a new layout of its benches. Ten workers are split at random into two groups of . The times to finish a task, in minutes, are , , , and with the old layout, and , , , and with the new one. These are made-up results. The manager suspects the new layout is faster. Find the observed difference in mean time, old minus new. Find how many splits of the times into two groups of there are. Find how many give a difference, first group minus second, at least as large as the observed one. Find the exact p-value to four decimal places, and decide at the level.
Need a reminder? The key ideaShow
If a treatment makes no difference, the group labels carry no information. Every split of the pooled values is then equally likely, and the p-value is the share of splits with a difference at least as large as the real one.
The worked solution
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Step 1. Observed. min.
Step 2. Splits. .
Step 3. Count. Listing all splits, give a difference of minutes or more.
Step 4. The p-value. .
Answer: minutes, splits, splits and a p-value of about .
Decision. , so we do not reject the null idea at the level. This does not show that the layout makes no difference. The study may simply be too small to tell.
Discussion (0)
Log in to join the discussion.
Loading…