Applied Statistics and Probability for Engineers

218 CHAPTER 6 RANDOM SAMPLING AND DATA DESCRIPTION

Trial 3 sistent with respect to the variability of the measurements?

Are all five trials centered on the same value? How does each

group of trials compare to the true value? Could there have

been “startup” effects in the experiment that Michelson

performed? Could there have been bias in the measuring

instrument?

6-86. In 1789, Henry Cavendish estimated the density of

the earth by using a torsion balance. His 29 measurements

follow, expressed as a multiple of the density of water.

5.50

5.55

5.57

5.34

5.42

5.30

5.61

5.36

5.53

5.79

5.47

5.75

4.88

5.29

5.62

5.10

5.63

5.86

4.07

5.58

5.29

5.27

5.34

5.85

5.26

5.65

5.44

5.39

5.46

880

880

880

910

880

850

860

870

720

840

720

840

620

850

860

840

970

840

950

840

Trial 4

890

910

810

920

810

890

820

860

800

880

770

720

760

840

740

850

750

850

760

780

Trial 5

890

870

840

870

780

810

810

740

760

810

810

940

790

950

810

800

820

810

850

870

The currently accepted true velocity of light in a vacuum is

299, 792.5 kilometers per second. Stigler (1977, The Annals of

Statistics) reports that the “true” value for comparison to these

measurements is 734.5. Construct comparative box plots of

these measurements. Does it seem that all five trials are con-

(a) Calculate the sample mean, sample standard deviation,

and median of the Cavendish density data.

(b) Construct a normal probability plot of the data. Comment

on the plot. Does there seem to be a “low” outlier in the

data?

(c) Would the sample median be a better estimate of the

density of the earth than the sample mean? Why?

c 06 .qxd 5/14/02 9:57 M Page 218 RK UL 6 RK UL 6:Desktop Folder:TEMP WORK:MONTGOMERY:REVISES UPLO D CH114 FIN L:Quark Files: