Question

A physiologist wishes to compare the effects of two concentrations of muscle relaxant on the quadriceps muscle in long-distance male runners. After acquiring ethical clearance, the researcher randomly selects 30 female long-distance runners (LDR) from a national list that included all male and female registered LDRs.

The researcher later marks a 7mm long muscle on the thigh (the rectus femoris which occupies the middle of the thigh) of each study participant and injects the higher concentration (in the marked muscle area) to 15 of the runners (randomly selected from the 30). The lower concentration is injected in the marked muscle area of the remaining 15 participants.

The researcher later measures the length of the marked muscle in all 30 participants after 15 minutes of the injection and she wants to conclude whether the two concentrations of drug differ in their effect. The estimate she will be using is the difference in sample means.

The results were as follows: the mean muscle length for the high concentration was 14 mm, and for the low concentration, 9.5 mm.

The researcher knew from previous large-scale research that the value of the population standard deviation for the effect of the high concentration of the relaxant drug on muscle was: σ_H=0.7 mm, and the population standard deviation for the low concentration was: σ_L=0.6 mm.

Question: Write a Null and an Alternative hypothesis for this trial and Calculate the difference in means of the two samples

Answer 1