SOLUTION: 13. A pharmaceutical firm claims that a new analgesic drug relieves mild pain under standard conditions for 3 hours, with a standard deviation 1 hour. Sixteen patients are tested u

Question 1200099: 13. A pharmaceutical firm claims that a new analgesic drug relieves mild pain under standard conditions for 3 hours, with a standard deviation 1 hour. Sixteen patients are tested under the same conditions and have an average pain relief time of 2.5 hours. Test the hypothesis that the population mean of this sample is actually 3 hours. Use ( =0.05). Try to follow all steps in hypothesis testing.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
population mean is equal to 3 hours.
population standard deviation is equal to 1 hour.
sample size is 16
sample mean is 2.5 hours.
standard error = standard deviation / square root of sample size = 1/4 = .25
at 95% two tailed confidence interval, critical z-score = plus or minus 1.96.
test z-score = (2.5 - 3) / .25 = -.5 / .25 = -2.
since the test z-score is more negative than the critical z-score, the test results are considered significant.
this indicates that there is a high probability that the actual mean is less than than 3 hours.

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