Question

The American Water Works Association reports that the per capita water use in a single family home is 76 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-seven owners responded, and the sample mean water use per day was 71 gallons with a standard deviation of 9.5 gallons per day. At the 0.01 level of significance, is that enough evidence to conclude that residents of Legacy Ranch use less water on average?

Answer 1

Answer)

Null hypothesis Ho : u = 76

Alternate hypothesis Ha : u < 76

As the population standard deviation is unknown here we will use t distribution to conduct the test

Test statistics t = (sample mean - claimed mean)/(s.d/√n)

t = (71 - 76)/(9.5/√27) = -2.735,

Degrees of freedom is = n-1 = 26

For 26 dof and -2.735 test statistics

P-value from t distribution is = 0.0055

Since the obtained P-value is less than the given significance 0.01

We reject the null hypothesis Ho

So, we have enough evidence to conclude that u < 76