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 6060 of the 830 830830 residential burglaries and 60 6060 of the 447 447447 commercial burglaries in the past year from their town database. Suppose that 65 % 65%65, percent of the residential burglaries and 31 % 31%31, percent of the commercial burglaries happened during the day. The company plans to look at the difference ( p ^ R − p ^ C ) ( p ^ R − p ^ C )left parenthesis, p, with, hat, on top, start subscript, start text, R, end text, end subscript, minus, p, with, hat, on top, start subscript, start text, C, end text, end subscript, right parenthesis between the proportions of daytime burglaries in each sample
