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

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 N, the standard deviation of the means based upon this data set (in m/s), the uncertainty, at 95 % confidence, in the estimate of the true mean value of the velocity (in m/s), and the interval about the sample mean over which 50 % of the data in this set will be (in m/s).

Explanation / Answer

Solution

Part (a)

Back-up Theory

For a sample drawn form a normal population, the sample size, N, required to estimate the population mean with an error margin of E, at 100(1 - )% confidence level is given by

N = (2.Z2 /2)/E2, where Z/2 = upper /2 percent point of Standard Normal distribution and is the standard deviation.

Now, to work out the solution,

In the given problem, = 0.1(i.e., 10%); = 1.5 and E = 2.61/2 = 1.305

From the Standard Normal Table, upper 5 percent point = 1.68.

Substituting these values, N = {(2.25 x 1.68)/1.305}2 = 8.6 ~ 9 ANSWER

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