Please, check the following problem from the exam:

exam problem

Could you check the following logic:

  1. H$_{0}$: difference in the ratings = 0
  2. H$_{a}$: difference in the ratings > 0, because human resources manager wants to determine an increase in the ratings
  3. Based on (2) I conclude that it is right-sided test and positive critical value of the test statistics is needed.

Am I right? Thanks.

  • $\begingroup$ Should have self study tag $\endgroup$ – Michael R. Chernick Dec 16 '16 at 12:47

You are correct the HR manager is testing for a positive change and therefore a one tail test is appropriate. However, the equation is


And therefore we are testing for a negative result (i.e. rating after are better than before - not very intuitive) and therefore a negative critical value is required at the 5% confidence level.

  • $\begingroup$ Is this a t test? Not specified in the exam problem. If it is you must know the degrees of freedom (should be pretty obvious) to determine which of the 4 answers is correct if any. $\endgroup$ – Michael R. Chernick Dec 16 '16 at 12:54
  • $\begingroup$ You could get the wrong answer if you get the degrees of freedom wrong or if you pick the wrong number of tails (1-tailed vs 2-tailed) test and a third wrong answer if you get both degrees of freedom and number of tails wrong. $\endgroup$ – Michael R. Chernick Dec 16 '16 at 13:00
  • $\begingroup$ I imagine those answering this may not even know about DoF. T-test is implied by the sample size. $\endgroup$ – Morgan Ball Dec 16 '16 at 13:12
  • 1
    $\begingroup$ So @MorganBall have we told the OP enough now so that he arrives at the right answer (maybe because he knows about df and what test is intended? I like your answer but whether or not I am hinting in a comment or an answer I worry that I am telling too much? $\endgroup$ – Michael R. Chernick Dec 16 '16 at 14:51
  • $\begingroup$ It seems that based on the sample size of the employees it follows that t-test is not appropriate hear and we should not use t-test. Right? $\endgroup$ – user190519 Dec 16 '16 at 16:15

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