Question

A company manager thinks he is overpaying for fertilizer at $175 per ton. To find out, he collects fertilizer prices per ton from five distributors.

a. Construct a 90% confidence interval for the true mean, given the following collected data:

[128, 140, 180, 166, 156]

b. Do you agree with the manager's thought? Why or why not?

Answer 1

a)

sample mean, xbar = 154
sample standard deviation, s = 20.5913
sample size, n = 5
degrees of freedom, df = n - 1 = 4

Given CI level is 90%, hence α = 1 - 0.9 = 0.1
α/2 = 0.1/2 = 0.05, tc = t(α/2, df) = 2.132

ME = tc * s/sqrt(n)
ME = 2.132 * 20.5913/sqrt(5)
ME = 19.63

CI = (xbar - tc * s/sqrt(n) , xbar + tc * s/sqrt(n))
CI = (154 - 2.132 * 20.5913/sqrt(5) , 154 + 2.132 * 20.5913/sqrt(5))
CI = (134.367 , 173.633)

b)

yes, because confidence interval does not contains 175

answered by: anonymous