The American Water Works Association reports that the per capita water use in a
ID: 3229011 • Letter: T
Question
The American Water Works Association reports that the per capita water use in a single-family home is 67 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-three owners responded, and the sample mean water use per day was 63 gallons with a standard deviation of 8.1 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: µ 67 when the test statistic is (Click to select)less thanmore than .
b. The value of the test statistic is . (Negative amount should be indicated by a minus sign. Round your answer to 3 decimal places.)
c. What is your decision regarding H0? Fail to reject Reject
Explanation / Answer
Given that,
population mean(u)=67
sample mean, x =63
standard deviation, s =8.1
number (n)=23
null, Ho: >=67
alternate, H1: <67
level of significance, = 0.025
from standard normal table,left tailed t /2 =2.074
since our test is left-tailed
reject Ho, if to < -2.074
we use test statistic (t) = x-u/(s.d/sqrt(n))
to =63-67/(8.1/sqrt(23))
to =-2.368
| to | =2.368
critical value
the value of |t | with n-1 = 22 d.f is 2.074
we got |to| =2.368 & | t | =2.074
make decision
hence value of | to | > | t | and here we reject Ho
p-value :left tail - Ha : ( p < -2.3683 ) = 0.01354
hence value of p0.025 > 0.01354,here we reject Ho
ANSWERS
---------------
null, Ho: >=67
alternate, H1: <67
test statistic: -2.368
critical value: -2.074
decision: reject Ho
p-value: 0.01354
enough evidence to conclude that residents of Legacy Ranch use less water on average
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