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 appropriate test statistic to test the hypotheses.
A)-0.38
B)2.43
C)0.38
D)-15.34
E)-2.43

Question

Quizplus · Accepted Answer

We need to use a one-sample t-test to test the hypotheses. The null hypothesis is that the population mean is equal to 123 gallons, and the alternative hypothesis is that the population mean is less than 123 gallons. We can calculate the t-statistic as:

t = (x̄ - μ) / (s / √n) = (113.03 - 123) / (25.99 / √40) = -2.43

where x̄ is the sample mean, μ is the hypothesized population mean, s is the sample standard deviation, and n is the sample size. The degrees of freedom are n-1=39. The t-value is -2.43, which corresponds to a p-value of 0.01. Since this p-value is less than the significance level of 0.05, we can reject the null hypothesis and conclude that there is evidence to suggest that the population mean is less than 123 gallons. Therefore, the best choice is E, -2.43.

It Is Estimated That the Average Person in the US