During an experiment, an aerospace engineering student measures a wind tunnel\'s

Question

During an experiment, an aerospace engineering student measures a wind tunnel's velocity N times. The student reports the following information, based on 90 % confidence, about the finite data set: mean velocity = 25.00 m/s, velocity standard deviation = 1.50 m/s, and uncertainty in velocity = 2.61 m/s. Determine (a) N, (b) the standard deviation of the means based upon this data set (in m/s), (c) the uncertainty, at 95 % confidence, in the estimate of the true mean value of, the velocity (in m/s), and (d) the interval about the sample mean over which 50 % of the data in this set will be (in m/s). An aerospace engineering student performs an experiment in a wind tunnel to determine the lift coefficient of an airfoil. The student takes 61 measurements of the vertical force using a force balance, yielding a sample mean value of 44.20 N and a sample variance of 4.00 N^2. Determine (a) the percent probability that an additional measurement will be between 45.56 N and 48.20 N, (b) the range (in N) over which the true mean value will be, assuming 90 % confidence, and (c) the range (in N^2) over which the true variance will be assuming 90 % confidence.

Explanation / Answer

Given that:

mean velocity=25.00m/s

sd.=1.5m/s

uncertainty=2.61m/s

a)calculate N:

N=(sd*ttable/margin of error)^2

ttable=t0.1=1.645 since 90% confidence

margin of error=uncertainty/mean=0.1044

therefore N=(1.5*1.645/0.1044)^2=558.61=559

b)Calculate standard deviation of mean:

V(Xbar=mean)=V(X)/N

V(X)=sd^2=1.5^2=2.25

N=559

V(Xbar)=2.25/559=0.004025

therefore standard deviation of mean=sqrt(V(Xbar)=0.0634

Related Questions

Navigate

• Browse (All)
• Browse D
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.