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	38	26	25	46	47	23	41	23	18	28	31	52
B	37	32	35	16	51	37	40	33	16	33	42	34

(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 thangreater than 0.10 or if t_calc <  or t_calc > .

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

t_calc            

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

p-value            

Answer 1

See the data collected on same person so this data pairs are dependent

For dependent data set we use pair t test.

Here we want to test "whether the evaluation teams are consistent or not".

Let's write null hypothesis (H₀) and altermative hypothesis(H₁)

Let's used excel :

Step 1) Enter the given data in excel columns.

Step 2) Click on Data >>>Data Analysis >>> t-Test: Pair Two sample for Means

then click on OK

In variable 1 Range select data of team A

In variable 1 Range select data of team B

Hypothesized mean difference : 0

Select Labels

Then click on Output range and select any empty cell

See the following box

Then click on OK

So we get the following output

From the above output we get,

p-value for two tailed = 0.861

t test statistic = -0.180

Critical values = -1.796 and t = 1.796  

Decision rule based on p-value:

Decision rule:

1) If p-value < level of significance (alpha) then we reject null hypothesis

2) If p-value > level of significance (alpha) then we fail to reject null hypothesis.

Here p value = 0.8607 > 0.10 so we used 2nd rule.

That is we fail to reject null hypothesis

Conclusion : At 10% of level of significance there was not sufficient evidence that the two teams are consistent.

So we can say that the two teams are consistent.