Question

In a test of the effectiveness of garlic for lowering​ cholesterol, 43 subjects were treated with garlic in a processed tablet form. Cholesterol levels were measured before and after the treatment. The changes in their levels of LDL cholesterol​ (in mg/dL) have a mean of 2.7 and a standard deviation of 16.3. Complete parts​ (a) and​ (b) below.

A. What is the best point estimate of the population mean net change in LDL cholesterol after the garlic​ treatment?

B. Construct a 90​% confidence interval estimate of the mean net change in LDL cholesterol after the garlic treatment. What does the confidence interval suggest about the effectiveness of garlic in reducing LDL​ cholesterol? What is the confidence interval estimate of the population mean muμ​?

C. What does the confidence interval suggest about the effectiveness of the​ treatment? Do they contain 0? Did it affect the cholesterol levels?

Answer 1

PART A.
given that,
best point estimate = sample mean, x =2.7

PART B.
standard deviation, s =16.3
sample size, n =43
i.
stanadard error = sd/ sqrt(n)
where,
sd = standard deviation
n = sample size
standard error = ( 16.3/ sqrt ( 43) )
= 2.486
ii.
margin of error = t α/2 * (stanadard error)
where,
ta/2 = t-table value
level of significance, α = 0.1
from standard normal table, two tailed value of |t α/2| with n-1 = 42 d.f is 1.682
margin of error = 1.682 * 2.486
= 4.181
iii.
ci = x ± margin of error
confidence interval = [ 2.7 ± 4.181 ]
= [ -1.481 , 6.881 ]
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direct method
given that,
sample mean, x =2.7
standard deviation, s =16.3
sample size, n =43
level of significance, α = 0.1
from standard normal table, two tailed value of |t α/2| with n-1 = 42 d.f is 1.682
we use ci = x ± t a/2 * (sd/ sqrt(n))
where,
x = mean
sd = standard deviation
a = 1 - (confidence level/100)
ta/2 = t-table value
ci = confidence interval
confidence interval = [ 2.7 ± t a/2 ( 16.3/ sqrt ( 43) ]
= [ 2.7-(1.682 * 2.486) , 2.7+(1.682 * 2.486) ]
= [ -1.481 , 6.881 ]

ho: no difference
ha: is a difference
ince 0 is in the ci, we fail to reject ho. no diffrence b/w before and after cholesterol levels

PART C.
the confidence interval limits contain 0., suggesting that the garlic treatment did not affect the cholesterol levels.