Lapsodiptia or Harnets (HD) disease afflicts about 50,000 people in the U.S. Rec

Question

Lapsodiptia or Harnets (HD) disease afflicts about 50,000 people in the U.S. Recently it has been discovered that there are two types of Harnets disease. At the Harnets Disease Research Center in Harpers Ferry, WV, scientists are developing a test to distinguish the differences between Type I and Type II Harnets disease. They want to measure different levels of diptoprotein in tissue surrounding the ears. These scientists feel that there is a difference in the mean levels of diptoprotein for the two types of HD. They sample tissue from 40 patients with Type I HD and 40 patients with Type II HD. For the former group they find that the mean diptoprotein level was 78.46 with a standard deviation of 9.24. For the Type II group, the mean level of diptoprotein was 84.26 with a standard deviation of 8.90. Using alpha = 0.05, test the hypothesis of interest.

Explanation / Answer

here we use z-test of difference of two samples mean

null hypothesis H0: mean1=mean2 and

alternate hypothesis H1: mean1 is not equal to mean2

z = |(x1- x2-)|/sqrt(12/n1+22/n2)=sqrt(|78.46-84.26|)/(9.24*9.24/40 + 8.9*8.9/40)=1.19

two tailed critical z(0.05)=1.96 is more than the calculated z=1.19, so we fail to reject H0 and conclude that

there is no difference between type I and Type II group

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