Question

Your company is developing a better means to eliminate cockroaches from buildings. In the process, your R&D team studies the absorption of sugar by these insects. They feed cockroaches a diet containing measured amounts of D-glucose. The cockroaches are killed at different times after eating, and the concentration of this sugar in various body parts is determined by a chemical analysis. Five cockroaches dissected after 10 hours had the following amounts (in micrograms) of D-glucose in their hindguts.

49.3, 55.6, 32.4, 27.8, 40.2

Find a 95% confidence interval for the mean amount of D-glucose in cockroach hindguts under these conditions.
(_____,_____)

Answer 1

sample mean, xbar = 41.06
sample standard deviation, s = 11.52
sample size, n = 5
degrees of freedom, df = n - 1 = 4

Given CI level is 95%, hence α = 1 - 0.95 = 0.05
α/2 = 0.05/2 = 0.025, tc = t(α/2, df) = 2.78

ME = tc * s/sqrt(n)
ME = 2.78 * 11.52/sqrt(5)
ME = 14.322

CI = (xbar - tc * s/sqrt(n) , xbar + tc * s/sqrt(n))
CI = (41.06 - 2.78 * 11.52/sqrt(5) , 41.06 + 2.78 * 11.52/sqrt(5))
CI = (26.74 , 55.38)