During laboratory testing of a cylindrical pressure vessel, the vessel’s diamete

Question

During laboratory testing of a cylindrical pressure vessel, the vessel’s diameter D was measured at 6 different locations generating the following data in units of inches, [9.50 9.31 9.15 9.08 9.62 9.82].

a) Determine the mean D and standard deviation SD for the above sample of diameter measurements.

b) Based on your sample calculation, determine the range in which the true mean diameter of the vessel is expected to fall with 95% confidence.

c) In part (b) you determined the range in which the true mean vessel diameter would fall with 95% confidence. A more conservative approach would be to determine the range of diameters found throughout the vessel. Estimate the range within which 95% of the diameter measurements will fall.

Explanation / Answer

a) mean = 9.41

SD = 0.285

b) DF = 5

At 95% confidence interval the critical value is t0.025, 5 = 2.571

The confidence interval is

mean +/- t0.025, 5 * sd/sqrt(n)

= 9.41 +/- 2.571 * 0.285/sqrt(6)

= 9.41 +/- 0.3

= 9.11, 9.71

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