Question 1174983
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I'll do the first problem to get you started.
You should only post one question at a time please.


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Part A


For the population of men undergoing the surgery, we have
xbar = 260 mg/dl = sample mean, used to estimate population mean (mu)
sigma = 40 mg/dl = population standard deviation
n = 100 = sample size


At 95% confidence, the z critical value is roughly z = 1.960
We're using the standard normal z distribution because we know the population standard deviation sigma.


The lower bound L of the confidence interval is:
L = xbar - z*sigma/sqrt(n)
L = 260 - 1.960*40/sqrt(100)
L = 260 - 7.84
L = 252.16


The upper bound U is
U = xbar + z*sigma/sqrt(n)
U = 260 + 1.960*40/sqrt(100)
U = 260 + 7.84
U = 267.84


The 95% confidence interval to estimate the mean population (mu) of the cholesterol level of the men undergoing surgery is (252.16, 267.84)
We are 95% confident that mu is somewhere in the interval (252.16, 267.84)


We can express that interval as 252.16 < mu < 267.84


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Part B


Yes we can conclude that the mean serum cholesterol for the men undergoing bypass surgery differs from the healthy men. 
This is because the interval 252.16 < mu < 267.84 does <u>not</u> contain mu = 240. This value is to the left of the lower bound 252.16


Since mu = 240 is not in the interval 252.16 < mu < 267.84, this means there's no way mu can be equal to 240 for the population of men undergoing surgery. 


In other words, if A and B represent the population means for the healthy men vs the men undergoing surgery, then we can say:
A = 240
B = some value between 252.16 and 267.84
clearly we can see that B = 240 is not possible and B > A and B > 252.16

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