The American Water Works Association reports that the per capita water use in a single family home is 73 gallons per day. Legacy Ranch is a relatively new housing development consisting of 100 homes. The builders installed more efficient water fixtures, such as low flush toilets, and subsequently conducted a survey of the residences. Thirty-nine homes responded, and the sample mean water use per day was 70 gallons with a standard deviation of 6.5 gallons per day.
At the .10 level of significance, is that enough evidence to conclude that residents of Legacy Ranch use less water on average?
(a) What is the decision rule? (Negative amount should be indicated by a minus sign. Round your answer to 3 decimal places.)
Reject H0 : μ ≥ 73 and fail to reject H1 : μ < 73 when the test statistic test is less than _____________
(b) The value of the test statistic is .