Question

A health care provider is testing that claim that a new pain reliever is better at reducing perceptible pain for patients after minor surgeries than a standard pain reliever. Assume that the standard pain reliever is known to bring relief in 15.5 minutes (? = 15.5) with standard deviation 3.5 minutes (? = 3.5).To test the hypothesis, n = 49 patients recovering from minor surgery were given the new pain reliever and the time they identified relief was recorded. The experiment produced a mean difference of 3.1 minutes. Using this information, determine whether there is sufficient evidence to indicate that the new pain reliever significantly reduced perceptible among patients following minor surgery; use ? = .05 when making your decision. For full credit include hypotheses, critical boundary, the standard error, z-score and final decision that includes an explanation of the results. Calculate Cohen’s d (if appropriate)

Answer 1

Answer)

Null hypothesis Ho : u = 15.5

Alternate hypothesis Ha : u < 15.5

As the population s.d is known here, we can use standard normal z table to conduct the test.

Test statistics z = (sample mean - claimed mean)/(s.d/√n)

Z = (-3.1)/(3.5/√49) = -6.2.

From z table, P(z<-6.2) = 0.

As the obtained P-value is less than the given significance 0.05.

We reject the null hypothesis Ho.

We have enough evidence to conclude that new pain reliever is better at reducing perceptible pain for patients after minor surgeries than a standard pain reliever.