Ten individuals went on a low-fat diet for 12 weeks to lower their cholesterol.

Question

Ten individuals went on a low-fat diet for 12 weeks to lower their cholesterol. The data are recorded in the table below. Do you think that their cholesterol levels were significantly lowered? Conduct a hypothesis test at the 5% level Starting cholesterol level Ending cholesterol level 150 200 110 240 200 180 190 360 280 260 150 230 130 220 190 150 200 300 300 240 NOTE: If you are using a Student's t-distribution for the problem, including for paired data, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.)

Explanation / Answer

Given that,
null, H0: Ud = 0
alternate, H1: Ud < 0
level of significance, = 0.05
from standard normal table,left tailed t /2 =1.833
since our test is left-tailed
reject Ho, if to < -1.833
we use Test Statistic  
to= d/ (S/n)
where
value of S^2 = [ di^2 – ( di )^2 / n ] / ( n-1 ) )
d = ( Xi-Yi)/n) = -4
We have d = -4
pooled variance = calculate value of Sd= S^2 = sqrt [ 5200-(-40^2/10 ] / 9 = 23.66
to = d/ (S/n) = -0.53
critical Value
the value of |t | with n-1 = 9 d.f is 1.833
we got |t o| = 0.53 & |t | =1.833
make Decision
hence Value of |to | < | t | and here we do not reject Ho
p-value :left tail - Ha : ( p < -0.5345 ) = 0.30297
hence value of p0.05 < 0.30297,here we reject Ho
ANSWERS
---------------
null, H0: Ud = 0
alternate, H1: Ud < 0
test statistic: -0.53
critical value: reject Ho, if to < -1.833
decision: Do not Reject Ho
p-value: 0.30297

cholwe don't have evidence that cholestrol level were significantly lowered

X Y X-Y (X-Y)^2 150 150 0 0 200 230 -30 900 110 130 -20 400 240 220 20 400 200 190 10 100 180 150 30 900 190 200 -10 100 260 300 -40 1600 280 300 -20 400 260 240 20 400 -40 5200

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