SOLUTION: A local hospital claims its ED mean wait time is less than 45 minutes. A random selection of the wait times of 40 patients is captured and the sample mean wait time is 44 minutes w

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Question 1086809: A local hospital claims its ED mean wait time is less than 45 minutes. A random selection of the wait times of 40 patients is captured and the sample mean wait time is 44 minutes with a sample standard deviation of 3.2 minutes. Assume they are approximately normally distributed. Is there enough evidence to support the claim at α = 0.01? Use a P-value. Will you accept or reject the null hypothesis based on these findings?
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
It's a one sample t-test.
Ho: ED wait >= 45 min
Ha: ED wait < 45 min
Test statistic is a t-test with t0.995,df=39 = -2.71
Assuming s is an adequate estimate of sigma,
t=(44-45)/3.2/sqrt (40)
=-1*sqrt(40)/3.2=-1.98
p-value is 0.0276
fail to reject Ho. The wait may be greater than or equal to 45 minutes at the 0.01 level.