Body fat and lean body mass can be estimated in living animals by measuring the
ID: 3220652 • Letter: B
Question
Body fat and lean body mass can be estimated in living animals by measuring the total body electrical conductivity (TOBEC). This technique is useful when attempting to determine if "diet drugs" are working on laboratory rats over time--the researchers need not sacrifice the animals to measure the amount of adipose body fat after periods of drug usage. However, the procedure requires that the animal be totally inside the measurement chamber, which is fairly small. Some rats are so big that their tails must be tucked under their bodies before putting them into the measurement chamber. This is causing concern among the researchers, because there is a possibility the tail position might alter the measurements. To see if the TOBEC measurement is altered by the tail position of the rats, an experiment was run on 16 rats ranging in weight from 210 to 505 g The rats were randomly assigned the order of measurement, with 8 rats measured in the tai under position first, and 8 rats in the tail-extended position. The data for the body fat measures, and the differences, are presented in the table belowExplanation / Answer
Tail-under and Tail-extended question, This is a paired comparison.
Ha: d 0
where d is the mean of the difference.
Mean of difference, d = 2.78125
Standard deviation, sd = sqrt [ ((di - d)2 / (n - 1) ] = 2.630391
Standard Error, SE = sd / sqrt( n ) = 2.630391/sqrt(16) = 0.65760
Degrees of freedom. DF = n - 1 = 16-1 = 15
Test statistic. t = (d - D) / SE = (2.78125 - 0)/0.65760 = 4.229
p-value = .000728
The result is significant at = 0.05.
There is sufficient evidence to reject the null hypothesis that the mean difference in body fat between tail extended and tail under positions is 0 and suggest the two tail positions cause a difference in body fat
Note:Please post the next question separately if it needs solving
Parameter of interest is mean of difference, dH0: d= 0