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 9 10 11 12 33 20 13 49 15 16 50 43 52 29 22 21 49 29 4 A 38 27 51 46 2320 47 40 (a) Choose the appropriate hypotheses. Assume μd 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 less than 0.10 or if fak (c) Find the test statistic tealc- (Round your answer to 3 decimal places. A negative value should be indicated by a minus sign.) (calc (d) Find the p-value. (Round your answer to 3 decimal places. A negative value should be indicated by a minus sign.) or tcalc (e) Make a decision. We Do not reject the null hypothesis. (f) State your conclusion. We can conclude that the evaluator teams are consistent in their estimates.

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D -0.667 D19.69 (1) Null and Alternative Hypotheses The following null and alternative hypotheses need to be tested This corresponds to a two-tailed test, for which a t-test for two paired samples be used (2) Rejection Region Based on the information provided, the significance level is 0.10, and the degrees of freedom are df 11 Hence, it is found that the critical value for this two-tailed test is tc-1.796, for α 0.10 and df The rejection region for this two-tailed test is R-{t: |t > 1.796) (3)_Test Statistics The t-statistic is computed as shown in the following formula 0.667 0.117 Sp/VT 19.69/vT2 Since it is observed that0.117 1.796, it is then concluded that the null hypothesis is not rejected Using the P-value approach: The p-value is p 0.9087, and since p-0.9087 > 0.10, it is concluded that the null hypothesis is not rejected (5) Conclusion It is concluded that the null hypothesis Ho is not rejected. Therefore, there is not enough evidence to claim that the population mean μ| is different than μ2, at the 0.10 significance level

a)
option A)
b)
p-value is less than 0.10
or t _Calc < -1.796 and t > 1.796
c)t_Calc = -0.117

d)
p-value = 0.9087
e)
we do not reject the null hypothesis
f)
we can conclude

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