Answer to Question #69007 in Statistics and Probability for Willis

Question

A pain reliever currently being used in a hospital is known to bring relief to patients in a mean time of 3.5minutes. To compare a new pain reliever with the one currently in use, the new drug is administered to a random sample of fifty patients’. The mean time to relief for the sample of patients is 2.8minutes and the variance is 1.3minutes.Do the data provide sufficient evidence to conclude that the new drug was effective in reducing the mean time until a patient receives relief from pain?. Test using p-value and let =0.10

Answer 1

Value of the test statistic t=(2.8-3.5)/(1.3/sqrt(50))= -3.807
p-value = P(T<-3.807)=P(T > 3.807)
p-value < 0.10
There is statistically significant evidence (at the 0.1 level) to conclude that the new drug lowers the mean time to pain relief.