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: Calculate the standard error for the difference of mean and the 95% confidence interval for the difference in means

sigma H means the drug higher concentration standard deviation while sigma L means the drug lower concentration standard deviation.
SIGMA H = standard deviation for higher concentration
SIGMA L = standard deviation for lower concentration.
Let me know if you need any additional information.

Answer 1

given that

sample size for High concentration=n1=15

The sample size for low concentration=n2=15

sample mean for high concentration =m1=14

sample mean of low concentration=m2=9.5

population standard deviation for high concentration =SD1=0.7

population standard deviation for low concentration=SD2=0.6

now standard error is given by

now 95% confidence interval for difference in mean is given by

we will use Z statistics as we know the population standard deviation

so interval is (4.0335,4.9665)