It is estimated that the average person in the US uses 123 gallons of water per day.Some environmentalists believe this figure is too high and conducted a survey of 40 randomly selected Americans.They find a mean of 113.03 gallons and a standard deviation of 25.99 gallons.Calculate the p-value for this test statistic.
A)0.4925
B)-0.0075
C)0.0075
D)0.015
E)0.352

Question

Quizplus · Accepted Answer

We will perform a one-sample t-test with the null hypothesis being that the population mean water usage is 123 gallons and the alternative hypothesis being that it is less than 123 gallons. Using a t-distribution with 39 degrees of freedom (n-1=40-1=39) and a t-statistic of (113.03-123)/(25.99/sqrt(40)) = -2.90, the p-value is found to be 0.0075 when looking at a one-tail test. Since we are interested in the alternative hypothesis that the population mean is less than 123 gallons, we only consider the left-tail of the t-distribution. The correct answer is therefore C).

It Is Estimated That the Average Person in the US