The changing ecology of swamps has been the subject of much environmental research. One water-quality parameter of concern is the total phosphorous level. Suppose that the Ministry of the Environment makes 15 measurements in one area of the swamp, yielding a mean level of total phosphorus of 12.3 parts per billion (ppb) and a standard deviation of 5.4 ppb. The Ministry wants to test whether the data support the conclusion that the mean level is less than 15 ppb. Assume measurements are normally distributed.
-The appropriate test statistic to test the hypotheses is _____.
A)7.50
B)1.94
C)3.88
D)-7.50
E)-1.94

Question

Quizplus · Accepted Answer

The test statistic for a one-sample t-test is calculated using the formula: $t = \frac{\bar{x} - \mu_0}{(s/\sqrt{n})}$, where $\bar{x}$ is the sample mean, $\mu_0$ is the hypothesized population mean, $s$ is the sample standard deviation, and $n$ is the sample size. Here, $\bar{x} = 12.3$ ppb, $\mu_0 = 15$ ppb, $s = 5.4$ ppb, and $n = 15$. Plugging these values into the formula gives $t = \frac{12.3 - 15}{(5.4/\sqrt{15})}$, which calculates to approximately -1.94.

The Changing Ecology of Swamps Has Been the Subject of Much