2. A random sample of n = 16 participants were selected from a normally distribu

Question

2. A random sample of n = 16 participants were selected from a normally distributed population of N = 200 conference attendees. The sample mean age was 36 years and population standard deviation = 8 years.

A) What is the standard error for these population where = 8 years and sample size of n=16 (hint use finite population correction factor)

B) What is the probability that the mean age of another sample from the same finite population will be 38 year or larger (x bar38)

C) What is the probability that the mean age of another sample from the same finite population will be 38 year or smaller (x bar 38)

D) What is approximately the largest sample mean of another sample of n=16 participants you would expect to obtain from this finite population (hints 99.8 %, z=3.09)

E) What sample mean of another sample n=16 participants from this finite population would you expect to be exceeded only 5% of the time (hint: upper tail = 5%)[MI1]

Explanation / Answer

a) = 8,x = 36
se = /sqrt(n) * sqrt((N-n)/(N-1))
se = 8/sqrt(16) * sqrt((200-16)/(200-1)) = 1.9231465

b) P(X <= 38) = P(Z <= (38 - 36)/1.9231465) = P(Z <= 1.03996) = 0.8508

c) P(X>=38) = 1- P(X <= 38) = 1-0.8508 = 0.1492

d) z = 3.09, z = (X - 38)/1.9231465 = 3.09, X = 43.9425

e) P(X >= x) = 0.05, Z = 1.645, z = (X - 38)/1.9231465 = 1.645, X = 41.16358

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