The American Water Works Association reports that the per ca

The American Water Works Association reports that the per capita water use in a single family home is 65 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-one homes responded, and the sample mean water use per day was 63 gallons with a standard deviation of 9.1 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?

What is the decision rule? (Negative amount should be indicated by a minus sign. Round your answer to 3 decimal places.)

The value of the test statistic is . (Negative amount should be indicated by a minus sign. Round your answer to 2 decimal places.)

Solution

(a) Given a=0.10, the critical value is Z(0.1) =-1.282 (from standard normal table)

Reject H₀ : mu= 65 and fail to reject H₁ : mu < 65 when the test statistic is less than -1.282 .

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(b)test statistic is

Z=(xbar-mu)/(s/vn)

=(63-65)/(9.1/sqrt(31))

=-1.22

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(c)Fail to reject