# EC315 - .,.

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Grand Strand Family Medical Center is specifically set up to treat minor medical emergencies for visitors to the Myrtle Beach area. There are two facilities, one in Little River Area and the other in Murrells Inlet. The Quality Assurance Department wishes to compare the mean waiting time for patients at the two locations. Samples of the waiting times, reported in minutes, follow: Assume the population standard deviation are not the same. At the .05 significance level, is there a difference in mean waiting time? H0: There is no difference in the mean waiting times at the two facilities, that is, m1 = m2 or m1 - m2 = 0 Ha: The mean waiting times at the two facilities are different, that is, m1 ≠ m2 or m1 - m2 ≠ 0 Two-tailed t- test for difference in population means; a = 0.05; DOF = 10 + 12 -2 = 20; Critical t- score = 2.0860 Decision Rule: Reject H0 if the test t- score < -2.0860 or > 2.0860 Little River Murrel's Inlet 31.73 22.93 28.77 23.92 29.53 26.92 22.08 27.2 29.47 26.44 18.6 25.62 32.94 30.61 25.18 29.44 29.82 23.09 26.49 23.1 26.69 22.31 n = 10 12 x-bar = 27.46 25.69 s = 4.44 2.68 Pooled Standard Deviation, S = sqrt [{(n1 - 1) * s1^2 + (n2 - 1) * s2^2}/(n1 + n2 - 2)] = sqrt [{(10 - 1) * 4.44^2 + (12 - 1) * 2.68^2}/20] = 3.5807 Standard Error, SE = S * sqrt{(n1 + n2)/(n1 n2)} = 3.5807 * sqrt{(10 + 12)/(10 * 12)} = 1.5332 t = (x1-bar - x2-bar)/SE = (27.46 - 25.69)/1.5332 = 1.1545 Since 1.1545 < 2.0860, we fail to reject H0 Conclusion: There is no sufficient evidence that the mean waiting times at the two facilities are different Location                                       Waiting time Little River    31.73   28.77   29.53   22.08   29.47   18.60   32.94   25.18   29.82   26.49

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