Is Garage B over-charging for car repairs?
10 cars go to Garage A and the other 10 go to Garage B.
The two sampling schemes are based on the same pool of 20 cars. See the description of the data for the distributions of the repair costs for each of these cars.
For each car, the estimate from Garage B is $200 more than the corresponding estimate from Garage A.
Use the first simulation to show that when the data are not paired — 10 cars are randomly selected to go to each garage — the 2-sample t-test often does not find evidence of a difference. (Click Show paired values to see the estimates that the garages would have given for all cars in grey. Of course only 20 of these values were actually observed.)
Explain that the variability between the cars overwhelms the difference between the garages.
Select Paired data and test from the pop-up menu then simulate several sets of paired data — 10 cars are randomly selected and are assessed by both garages. When the data are collected in this way (and analysed with a paired t-test), there is usually strong evidence that Garage B gives higher estimates.
The simulation is based on a pool of 20 cars with estimated repair costs that are normal (µ, σ = $120) where µ is shown below:
Mean repair estimate, µ ($) | |||||
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Car | Garage A | Garage B | |||
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The two sampling schemes sample from the same cars.