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RAMweb Colorado State × e Home | Chegg.com C) Lab 9.pdf: 2017FA-STAT- x, D Lab 9.pdf x C file:///C/Usersjohnw/Downloads.Lab%209.pdf 1. A certain lake containing the invasive species zebra mussels is considered "healthy" if the average number of zebra mussels per acre is less than or equal to 100,000. If the average is larger than 100.000, the lake is (a) 2 pts) Write down the appropriate null and alternative hypotheses corresponding to the lake being healthy" or "infested" (c) t (d) 12 pts) In the context of the problem, explain the Type Il error and the consequences of making this error Type here to search e" 11/2/2017Explanation / Answer
If the average number of zebra mussels per acre is less than 100000, then the lake is considered to be healthy. If it is more, then the lake is infested.
Suppose the average number of zebra mussels per acre in the lake be denoted by "mu". A sample is collected and the count is evaluated.
(a) Here we want to test the hypothesis,
H0 : mu = 100000 vs H1: mu > 100000
The null hypothesis represents that the lake is healthy whereas the alternative represents it is infested.
(b) The null hypothesis may be true or may be false (in which case the alternative is true). The decision regarding the test may be rejecting or accepting the null hypothesis. The table is representing the correct decisions, type-I error and type-II error:
(c) Type-I error is associated with the rejection of true null. Here the null hypothesis represents that the lake is healthy. Otherwise, the lake will be treated with pesticides by which all aquatic fauna will be killed. If the null hypothesis is true but the decision of rejection of H0 is taken, then pesticide will be applied wrongly when in fact the lake is healthy. This error wrongly kills all the aquatic fauna which is ethically wrong.
(d) Type-II error is associated with the acceptance of false null. Here the false null or true alternative is that the lake is infested for which case pesticides need to be applied. If the false null is accepted, that is the lake is infested but the decision is taken that no pesticide is needed to apply, the that associates the type-II error. For this case, although the lake needs to be cleaned by pesticides, it is not applied. This is not that severe like type I error.
H0 is rejected H0 is accepted H0 is true Type - I error Correct decision H1 is true (H0 is false) Correct decision Type - II errorRelated Questions
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