A security system company wants to know whether there are differences in the time of day of residential and commercial burglaries. They read the records from a randomly selected sample of 60 of the 830 residential
burglaries and 60 of the 447 commercial burglaries in the past year from their town database.
Suppose that 65% of the residential burglaries and 31% of the commercial burglaries happened during the day.
The company plans to look at the difference (Pr - Pc) between the proportions of daytime burglaries in each
sample.
Consider the formula:
PA (1-PA)
PE (1 - PB
OPAPU
1
MA
NB
Why is it not appropriate for the company to use this formula for the standard deviation of Pr - pc?