In a newspaper article entitled \"Criminal Pasts Cited for Many City School Bus

Question

In a newspaper article entitled "Criminal Pasts Cited for Many City School Bus Driver s," it is reported that "state auditors checking the records of a random sample of 100 city bus drivers have found that more than a quarter of them had criminal histories... A series of problems last year with school bus drivers... prompted [state Auditor General] Casey to take a closer look at the city's staff of 750 drivers..."4 Show that our rule of thumb for approximate independence for sampling without replacement is not quite satisfied.

Explanation / Answer

The rule of thumb for approximate independece is as follows.

"When sampling without replacement, random selections are approximately independent as long asthe populationis at least 10 times the sample size"

For the given problem sample size is 100

and population size is 750

i.e., 750 is less than 10 times of 100 i.e., 750 <10*100 =1000.

Hence for the given problem the rule of thumb for approximate independece is not quite satisfied.

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