Question

Truckloads of waste contaminated with cadmium may either be sent to a sanitary landfill or a...

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.

Math   Statistics-And-Probability   
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Answer #1

ANSWER:

Given that,

The hypotheses are:

because we need to see if

2)

right tailed , because the H1 is in the

right tailed ,that is our rejection region

3)

it does no matter ,but we prefer a sample size large because they have a behavior like the population

4)

Type I error : reject Ho, when ho is true

this error implicates that you conclude that the mean is greater than 1 when actually mean is less than 1

but as you conclude that you will the trucks must be sent further to the hazardous landfill

Type II error : accept Ho, when Ho is false

this error implicates that you conclude that mean is less than 1 , when actually mean is greater than 1

the consequence will be that you will have waste contaminated with cadmium

5)

the mean level of cadmium on today's truckloads is less than 1

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