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.

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

Click here for the Excel Data File

(a) Choose the appropriate hypotheses to test for a difference between the teams. Assume μ_d is the difference in mean lengths of team A and team B.

• H₀: μ_d = 0 vs. H₁: μ_d ≠ 0

• H₀: μ_d ≥ 0 vs. H₁: μ_d < 0

• H₀: μ_d ≤ 0 vs. H₁: μ_d > 0

(b) Specify the decision rule at the .10 level of significance.

Reject the null hypothesis if the p-value is  (Click to select)  less than  greater than  .10 .

You will need to copy and paste the data from Excel into Minitab.

(c) Find the test statistic t_calc. (Use Minitab. Round your answer to 4 decimal places. A negative value should be indicated by a minus sign.)

t_calc            

(d) Find the p-value. (Use Minitab. Round your answer to 3 decimal places.)

p-value            

(e) Make a decision.

We  (Click to select)  Do not reject  Reject  the null hypothesis.

(f) State your conclusion.

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

Answer 1

(a) Choose the appropriate hypotheses to test for a difference between the teams. Assume μ_d is the difference in mean lengths of team A and team B.

• H₀: μ_d = 0 vs. H₁: μ_d ≠ 0

(b) Specify the decision rule at the .10 level of significance.

at df = 12 - 1= 11

and alpha = 0.1

Reject H0 if |t| > 1.795

(c) Find the test statistic t_calc.

team	A	B	Difference
1	37	28	9
2	18	22	-4
3	52	44	8
4	19	48	-29
5	45	48	-3
6	40	23	17
7	51	48	3
8	31	43	-12
9	41	23	18
10	39	33	6
11	32	18	14
12	33	16	17
		Mean	3.666667
		s	13.93709
		n	12

t = 0.9114

(d) Find the p-value.
p-value = 0.1207

(e) Make a decision.

As p < alpha

Do not reject   the null hypothesis.

(f) State your conclusion.

We can conclude that the evaluator teams are consistent in their estimates.