# STATISTICS WITH EXPLANATION

Truckloads of waste contaminated with cadmium may either be sent to a sanitary landfill or a hazardous waste landfill. The levels of cadmium vary daily so each morning a sample of truckloads must be tested to determine which landfill to use. If the mean level of cadmium exceeds the allowable amount of 1 milligram per liter for a sanitary landfill then the trucks must be sent further to the hazardous landfill. Of course, driving a further distance requires more expense for the company. You are in charge of testing and determining which landfill to use for dumping for today.

You will use a 5% level of significance for your hypothesis test.

1. State the null and alternative hypotheses, and identify which represents the claim. Why?

2. Determine the type of test that you should use: left-tailed, right-tailed, or two-tailed. Explain your reasoning.

3. What sampling technique would you use to determine your sample of truckloads that will be tested this morning? Should a small sample or a large sample be used? Does it really matter?

4. What decision concerning your null hypothesis would result in a Type I error? What is the interpretation and the implication of this error? What about a Type II error? Obviously, you want to minimize the risk of both types of error when decision making. Which of these errors is more serious in this situation?

5. Suppose that the null hypothesis is rejected when you perform your hypothesis test. Assuming that a correct decision was made, what do you believe regarding the mean level of cadmium on today’s truckloads? Give a complete interpretation.