Question

1. In order for oil to be labeled “no trans-fat,” the mean trans-fat content per serving should be less  than 0.4 milligrams.  A new type of oil was developed, and marketing was hopeful that the oil would meet the “no trans-fat” criteria.  Let  represent the mean trans-fat content per serving  for the new oil.                                       

The following are the hypotheses:

H_o:  = 0.4 mg  (The new oil does not meet the “no trans-fat” criteria.)        

H_a:   < 0.4 mg (The new oil meets the “no trans-fat” criteria.)                                 

      a.  State the Type I error for this example.   

                Type I error: reject Ho when Ho is true(definition)                                                                                                                                               

      b.  State the Type II error for this example.

Type II error: Fail to reject Ho when Ho is false(definition)                                                                                  

3. Which type of error would a consumer who is on a no trans-fat diet view as

more serious?    Explain.

2. The proportion of professional baseball players who take steroids has been assumed to be twenty percent by the team owner council. The Commissioner of Baseball has instituted a new campaign to reduce the proportion of players who take steroids.  The Commissioner would now like to test whether their campaign has worked. (α = 0.05)

      State the null and alternative hypotheses that the Commissioner would test. Use

      symbols in the hypotheses. State alpha and define the parameter.

H_o:  p = 0.2  (.)   

H_a:  p < 0.2 (.)                                 

Answer 1

1.

A.

Type 1 error: Accepting that the new oil is “no trans-fat” even though it is not.

B.

Type 2 error: Accepting that the new oil does not meet the “no trans-fat” even though it does.

C.

Type 1 error because he would consume the new oil assuming that it is “no trans-fat” when actually it was not.

2.

α = 0.05

The alpha level is the probability of rejecting the null hypothesis when the null hypothesis is true i.e. probability of considering that the campaign has worked when infact it has not.

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