In hamilton county ohio the mean number of days needed to sell a home is 86 days (cincinnati multiple listing service, april, 2012). data for the sale of 40 homes in a nearby county showed a sample mean of 80 days with a sample standard deviation of 20 days. conduct a hypotheses test to determine whether the mean number of days until a home is sold is different than the hamilton county mean of 86 days in the nearby county. round your answer to four decimal places.