Question

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. twenty-five owners responded, and the sample mean water use per day was 64 gallons with a standard deviation of 7.1 gallons per day.at the 0.10 level of significance, is that enough evidence to conclude that residents of legacy ranch use less water on average?

Answer 1

To determine if residents of Legacy Ranch use less water on average, a hypothesis test is performed. The results show enough evidence to conclude that residents of Legacy Ranch use less water on average.

Step-by-step explanation:

To determine if residents of Legacy Ranch use less water on average, we can perform a hypothesis test. The null hypothesis (H0) assumes that the average water use is equal to 69 gallons per day, while the alternative hypothesis (H1) assumes that the average water use is less than 69 gallons per day.

We will use a one-sample t-test with a significance level of 0.10.

To perform the hypothesis test, we calculate the test statistic using the formula:

t = (sample_mean - population_mean) / (sample_standard_deviation / sqrt(sample_size))

Plugging in the values from the survey:

t = (64 - 69) / (7.1 / sqrt(25))

t = -5 / (7.1 / 5)

t = -5 / 1.42

t = -3.52

Next, we compare the test statistic to the critical value from the t-distribution table. For a one-tailed test at a significance level of 0.10 and 24 degrees of freedom, the critical value is approximately -1.318.

Since the test statistic (-3.52) is less than the critical value (-1.318), we reject the null hypothesis.

Therefore, there is enough evidence to conclude that residents of Legacy Ranch use less water on average.