You will be asked to determine thecorrect decision (Reject Ho or Fail to Reject

Question

You will be asked to determine thecorrect decision (Reject Ho or Fail to Reject Ho) for each of thefollowing tests of hypotheses. (3 points each)

a. Ahypothesis test at the 0.025 level of significance with a p-valuefor the sample of 0.0075.

b. Ahypothesis test at the 0.01 level of significance with a p-valuefor the sample of 0.0122.

c. Atwo-tailed hypothesis test at the 0.10 level of significance wherethe initial probability calculated for the test statistic is0.047. (Don’t forget to make the adjustment needed forthe two tailed test.)

d. Atwo-tailed hypothesis test with critical values of ±2.33 anda test statistic for the sample of -2.56.

e. A one tailed hypothesis test with a critical value of1.383 and a test statistic for the sample of 1.625.

f. A one tailed hypothesis test with a critical value of-1.648 and a test statistic for the sample of-1.023.  

Explanation / Answer

The decision rule for any test of hypothesis is as follows, ifP - value < , we reject our H0 ,otherwise we fail to reject
our H0 at level of significance. If test statistic > ctitical value or test statistic < -critical value for a two tailed test we reject our H0 ,otherwise we fail to reject our H0 at level ofsignificance. If test statistic > ctitical value for a right tailedtest we reject our H0 , otherwise we fail to reject ourH0 at level of significance. If test statistic < critical value fora left tailed test we reject our H0 , otherwise wefail to reject our H0 at level ofsignificance. a) Reject our H0 , since 0.0075 < 0.025 b) Fail to reject our H0 , since 0.0122 > 0.01 c) Reject our H0  , since 0.094 <0.10 d) Reject our H0 , since -2.56 < -2.33 e) Reject our H0 , since 1.625 > 1.383 f) Fail to reject our H0 , since -1.023 >-1.648

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