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 79 gallons per day. Legacy Ranch is a relatively new housing development. The builders installed more efficient water fixtures, such as low-flush toilets, and subsequently conducted a survey of the residences. Twenty owners responded, and the sample mean water use per day was 77 gallons with a standard deviation of 9.0 gallons per day. At the 0.025 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: 79 and fail to reject H1: < 79 when the test statistic is _____________ .

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

c. What is your decision regarding H0?

Reject

Fail to reject

Solution

a)

Formulating the null and alternative hypotheses,              
              
Ho:   u   >=   79  
Ha:    u   <   79  
              
As we can see, this is a    left   tailed test.      
              
Thus, getting the critical t,              
df = n - 1 =    19          
tcrit =    -   2.093024054      

Thus,

Reject Ho when t < -2.093 [ANSWER]

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b)
              
Getting the test statistic, as              
              
X = sample mean =    77          
uo = hypothesized mean =    79          
n = sample size =    20          
s = standard deviation =    9          
              
Thus, t = (X - uo) * sqrt(n) / s =    -0.99380799 = -0.99   [ANSWER]

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c)      

As |t| < 2.093, then we FAIL TO REJECT HO.