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 69 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. Thirty - six homes responded, and the sample mean water use per day was 64 gallons with a standard deviation of 6.2 gallons per day. At the .01 level of significance, is that enough evidence to conclude that residents of Legacy Ranch use less water on average? (Please use MegaStat to solve the problem)

Solution

Let mu be the population mean

The test hypothesis:

Ho: mu=69 (i.e. null hypothesis)

Ha: mu<69 (i.e. alternative hypothesis)

The test statistic is

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

=(64-69)/(6.2/sqrt(36))

=-4.84

It is a left-tailed test.

Given a=0.01, the critical value is Z(0.01) =-2.33 (from standard normal table)

The rejection region is if Z<-2.33, we reject the null hypothesis.

Since Z=-4.84 is less than -2.33, we reject the null hypothesis.

So we can conclude that enough evidence to conclude that residents of Legacy Ranch use less water on average