A cognitive retraining clinic assists outpatient victims of head injury, anoxia,

Question

A cognitive retraining clinic assists outpatient victims of head injury, anoxia, or other conditions that result in cognitive impairment. Each incoming patient is evaluated to establish an appropriate treatment program and estimated length of stay. To see if the evaluation teams are consistent, 12 randomly chosen patients are separately evaluated by two expert teams (A and B) as shown.

  

(a) Choose the appropriate hypotheses. Assume d is the difference in mean lengths of team A and team B.

(b) Specify the decision rule at the .10 level of significance.(Round your answers to 3 decimal places. A negative values should be indicated by a minus sign.)

Reject the null hypothesis if the p-value is (greater than or less than) 0.10 or if tcalc < ______ or tcalc >_______ .

(c) Find the test statistic tcalc. (Round your answer to 3 decimal places. A negative value should be indicated by a minus sign.)

tcalc            

(d) Find the p-value. (Round your answer to 3 decimal places. A negative value should be indicated by a minus sign.)

p-value            

(e) Make a decision.

We (Do not reject or Reject) the null hypothesis.

(f) State your conclusion.

We (can or cannot) conclude that the evaluator teams are consistent in their estimates.

  Estimated Length of Stay in Weeks Patient   Team 1 2 3 4 5 6 7 8 9 10 11 12   A 37 18 52 19 45 40 51 31 41 39 32 23   B 28 22 44 48 48 23 48 43 23 33 18 16

Explanation / Answer

a)

H0: d = 0 vs. H1: d 0

b)

Reject the null hypothesis if the p-value is (greater than or less than) 0.10 or if tcalc < -1.7959 or tcalc > 1.7959.

c)

dbar = 17

s(dbar) = 13.3542

SE = s(dbar)/sqrt(n) = 3.8550

Test Statisitcs, t = dbar/SE = 4.4098

d)

degrees of freedom = n-1 = 11

p-value = 0.0010

Excel formula to calculate p-value: =2*(1-T.DIST(4.4098,11,TRUE))

e)

Reject null hypothesis

f)

We cannot conclude that the evaluator teams are consistent in their estimates.

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