A large metropolitan bank has analyzed the amount of time required to process
home loans and determined that the times follow a normal distribution with
mean time μ = 45 hours. The bank's operations manager has developed a new
procedure for processing the loans which involves extensive use of new
computer software. He believes that the new procedure will decrease the
population mean amount of time required to process home loans. After training
a group of loan officers, a random sample of 25 loan applications will be
selected and the average amount of time required to process the loans will be
determined. If the switch is made to the new procedure, the cost of the
additional software will be more than offset by the savings in manpower
required to process the loans. Use the hypotheses H0 : μ ≥ 45 hours and
Ha :μ < 45 hours.
Due to the importance of this decision, the operations manager makes some
adjustments in the procedure and decides to look at another random sample of
25 loan applications. If the population mean time required to process a loan has
in fact been reduced to μ = 41.2 hours with σ = 5.5 hours, what is the
probability that the test will indicate that there has been no decrease in the
population mean time? (Note: The test will still be done using α = .025.)
Round your answer to 4 decimal places. (10%)
One indication of how strong the real estate market is performing is the
proportion of properties that sell in less than 30 days after being listed. Of the
condominiums in a Florida beach community that sold in the first six months of
2006, 75 of the 115 sampled had been on the market less than 30 days. For the
first six months of 2007, 25 of the 85 sampled had been on the market less than
30 days. Test the hypothesis that the proportion of condominiums that sold
within 30 days decreased from 2006 to 2007. Use α = .01. (10%)
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