Question

You are an analyst working for the life cycle manager of a particular type of cruise missile. Periodically, the inventory of cruise missile engines must be certified and part of the certification requires testing a sample of missile engines then calculating a confidence interval for the true mean flight speed (μ in mph). Based on prior tests, it is appropriate to assume that the missile’s flight speed is normally distributed with known standard deviation, σ=20 mph.

Twenty-five cruise missiles are tested on a range with an average flight speed of?1=375 mph. You are tasked to calculate a 90 percent confidence interval for ?.

Fill in the table to help document your work:

sigma
n
y-bar
se(y-bar)
CI
alpha
alpha/2
Z, alpha/2
Half-width (margin of error)
Upper Bound
Lower Bound

Answer 1

The confidence interval is calculated as

The formula for estimation is:

μ = ± Z(s_M)

where:

= Population standard deviation

= sample mean
Z = Z statistic determined by confidence level using Z table shown below
S = standard error = √(²/n)

= 375
Z = 1.65
S = √(20²/25) = 4

μ = ± Z(S)
μ = 375 ± 1.65*4
μ = 375 ± 6.6

90% CI [368.4, 381.6].

sigma	20
n	25
y-bar	375
se(y-bar)	4
CI	368.4, 381.6
alpha	0.1
alpha/2	0.05
Z, alpha/2	1.65
Half-width (margin of error)	6.6
Upper Bound	368.4
Lower Bound	381.6

Z table