Question

The cholesterol levels of a random sample of 250 men are measured. The sample mean is 182 and the sample standard deviation is 32.

a.)Give the value of the point estimate of the mean cholesterol level for men.

b.) Give the value of the standard error of the mean cholesterol level for men.

c.) Give the value of the margin of error of the mean cholesterol level for men for a 95% confidence interval.

d.)Give the value of the point estimate of the mean cholesterol level for men in interval notation.

Answer 1

a)

Point stimate = sample mean, xbar = 182

b)

sample standard deviation, s = 32
sample size, n = 250

standard error = 32/sqrt(250) = 2.0239

c)

degrees of freedom, df = n - 1 = 249

Given CI level is 95%, hence α = 1 - 0.95 = 0.05
α/2 = 0.05/2 = 0.025, tc = t(α/2, df) = 1.97

ME = tc * s/sqrt(n)
ME = 1.97 * 32/sqrt(250)
Margin of errro = E = 3.987

d)

CI = (xbar - tc * s/sqrt(n) , xbar + tc * s/sqrt(n))
CI = (182 - 1.97 * 32/sqrt(250) , 182 + 1.97 * 32/sqrt(250))
CI = (178.01 , 185.99)

point estimate of the mean cholesterol level for men in interval notation. = 32 +/- 3.987