The administrator at your local hospital states that on weekends the average wai

Question

The administrator at your local hospital states that on weekends the average wait time (assume waiting times are normally distributed) for emergency room visits is 10 minutes. Based on discussions you have had with friends who have complained on how long they waited to be seen in the ER over a weekend, you dispute the administrator's claim. You decide to test your decide to test your hypothesis. Over the course of a few weekends you record the wait time for 40 randomly selected patients. The average wait time for these 40 patients is 11 minutes with a standard deviation of 3 minutes. Do you have enough evidence to support your hypothesis that the average ER wait time exceeds 10 minutes? You opt to conduct the test at a 5% level of significance. Perform a formal hypothesis testing.

Explanation / Answer

here null hypothesis : mean<=10 minutes

alternate hypothesis: mean >10 minutes

for 0.05 level of significance and 39 degree of freedom ; rejection region: tstat>1.6849

std error of mean =std deviation/(n)1/2 =0.4743

hence test stat t=(X-mean)/std error =(11-10)/0.4743 =2.1082

as our test stat is higher then critical value ; hence falls in rejection region ; therefore we reject null hypothesis.

And conclude that average ER wait time exceeds 10 minutes

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