Two hospital emergency rooms use different procedures for triage of their patients.We want to test the claim that the mean waiting time of patients is the same for both hospitals.The 40 randomly selected subjects from one hospital produce a mean of 18.3 minutes.The 50 randomly selected patients from the other hospital produce a mean of 25.31 minutes.Assume a $\sigma$_a = 2.1 minutes and $\sigma$_b = 2.92 minutes.Calculate the test statistic for testing these hypothesis. A)-21.05 B)-24.97 C)-13.24 D)-18.49

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Quizplus · Accepted Answer

The test statistic is calculated using the formula for the difference between two means with known standard deviations: $ Z = \frac{\bar{X}_1 - \bar{X}_2}{\sqrt{\frac{\sigma_1^2}{n_1} + \frac{\sigma_2^2}{n_2}}} $. Plugging in the values: $ Z = \frac{18.3 - 25.31}{\sqrt{\frac{2.1^2}{40} + \frac{2.92^2}{50}}} \approx -13.24 $.

Two Hospital Emergency Rooms Use Different Procedures for Triage of Their