Question

Painadol is a well trusted, popular pain-killer used by millions throughout the country. Recently an epidemic of headaches has hit the nation and the manufacturers of Painadol have created a new, stronger painkiller called Painadene. The manufacturers are interested in testing whether the speed of pain relief is different with Painadene. It is known that the mean time taken by Painadol tablets to relieve pain is 26 minutes and the standard deviation is 6 minutes. The manufacturers would like to construct a hypothesis test for the mean time (μ) taken for Painadene tablets to relieve pain assuming the same population standard deviation (σ) as the Painadol tablets. A random sample of 36 people with headaches tried the new Painadene tablets and the mean time taken to relieve the pain was calculated as 24 minutes. The hypotheses that will be used by the manufacturers are H0: μ = 26 and Ha: μ ≠ 26. a)Calculate the test statistic (z) that corresponds to the sample and hypotheses. Give your answer as a decimal to 3 decimal places. z = -2 b)Using the test statistic for Painadol's hypothesis test and level α = 0.1, Painadol should the null hypothesis.

Answer 1

(a) The value of Z is -2.

(b) We accept the null- hypothesis.

Explanation:

(a) We have,Null Hypothesis(H₀): μ = 26

and Alternative Hypothesis (Hₐ): μ ≠ 26.

Now, Calculating the value of Z-test:

Z = (M - μ) ÷ (σ / √n)

Z = (24 - 26) ÷ (6 / √36)

Z = -2 / 1

Z = -2

(b) The value of Z is -2.

The value of p is .0455 at α = 0.1.

The result is significant at p < .05.

Hence, We accept the null- hypothesis.