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 24 24 52 30 40 30 18 30 18 40 24 12 B 24 20 52 36 36 24 36 16 52 24 24 16 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. a. H0: μd ≤ 0 vs. H1: μd > 0 b. H0: μd ≥ 0 vs. H1: μd < 0 c. H0: μd = 0 vs. H1: μd ≠ 0 a b c (b) Specify the decision rule at the .10 level of significance. (Round your answers to 3 decimal places. Negative values should be indicated by a minus sign.) Reject the null hypothesis if the p-value is (Click to select) greater than less 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.
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
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 | 24 | 24 | 52 | 30 | 40 | 30 | 18 | 30 | 18 | 40 | 24 | 12 |
| B | 24 | 20 | 52 | 36 | 36 | 24 | 36 | 16 | 52 | 24 | 24 | 16 |
(a) Choose the appropriate hypotheses. Assume μd is the difference in mean lengths of team A and team B.
a. H0: μd ≤ 0 vs. H1: μd > 0
b. H0: μd ≥ 0 vs. H1: μd < 0
c. H0: μd = 0 vs. H1: μd ≠ 0
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a
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b
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c
(b) Specify the decision rule at the .10 level of significance. (Round your answers to 3 decimal places. Negative values should be indicated by a minus sign.)
Reject the null hypothesis if the p-value is (Click to select) greater than less 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.
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