In: Statistics and Probability
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.
Estimated Length of Stay in Weeks | ||||||||||||
Patient | ||||||||||||
Team | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
A | 22 | 30 | 15 | 34 | 14 | 47 | 35 | 19 | 35 | 25 | 21 | 29 |
B | 33 | 35 | 39 | 41 | 23 | 47 | 19 | 28 | 38 | 33 | 19 | 33 |
Click here for the Excel Data File
(a) Choose the appropriate hypotheses. Assume
μd is the difference in mean lengths of team A
and team B.
H0: μd ≥ 0 vs. H1: μd < 0
H0: μd = 0 vs. H1: μd ≠ 0
H0: μd ≤ 0 vs. H1: μd > 0
(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 (Click to select) less
than greater than .10 or if
tcalc < or
tcalc > .
(c) Find the test statistic
tcalc. (Round your answer to 4 decimal
places. A negative value should
be indicated by a minus sign.)
tcalc
(d) Find the p-value. (Round your
answer to 4 decimal places. A
negative value should be indicated by a minus
sign.)
p-value
(e) Make a decision.
We (Click to select) Reject Do not
reject the null hypothesis.
(f) State your conclusion.
We (Click to
select) cannot can conclude that
the evaluator teams are consistent in their estimates.