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216 CHAPTER 6 RANDOM SAMPLING AND DATA DESCRIPTION

6-71. Construct two normal probability plots for the height (a) Calculate the sample range for both samples. Would you
data in Exercises 6-22 and 6-29. Plot the data for female and conclude that both samples exhibit the same variability?
male students on the same axes. Does height seem to be Explain.
normally distributed for either group of students? If both pop- (b) Calculate the sample standard deviations for both sam-
ulations have the same variance, the two normal probability ples. Do these quantities indicate that both samples have
plots should have identical slopes. What conclusions would the same variability? Explain.
you draw about the heights of the two groups of students from (c) Write a short statement contrasting the sample range
visual examination of the normal probability plots? versus the sample standard deviation as a measure of vari-
6-72. It is possible to obtain a “quick and dirty” estimate of ability.
the mean of a normal distribution from the fiftieth percentile 6-76. An article in Quality Engineering (Vol. 4, 1992, pp.
value on a normal probability plot. Provide an argument why 487–495) presents viscosity data from a batch chemical
this is so. It is also possible to obtain an estimate of the stan- process. A sample of these data follows:
dard deviation of a normal distribution by subtracting the
sixty-fourth percentile value from the fiftieth percentile value. 13.3 14.3 14.9 15.2 15.8 14.2 16.0 14.0
Provide an argument why this is so.
14.5 16.1 13.7 15.2 13.7 16.9 14.9 14.4
15.3 13.1 15.2 15.9 15.1 14.9 13.6 13.7
6-8 MORE ABOUT PROBABILITY 15.3 15.5 14.5 16.5 13.4 15.2 15.3 13.8
PLOTTING (CD ONLY) 14.3 12.6 15.3 14.8 14.1 14.4 14.3 15.6
14.8 14.6 15.6 15.1 14.8 15.2 15.6 14.5
Supplemental Exercises 15.2 14.3 15.8 17.0 14.3 14.6 16.1 12.8
14.5 15.4 13.3 14.9 14.3 16.4 13.9 16.1
6-73. The concentration of a solution is measured six times 14.6 15.2 14.1 14.8 16.4 14.2 15.2 16.6
by one operator using the same instrument. She obtains the 14.1 16.8 15.4 14.0 16.9 15.7 14.4 15.6
following data: 63.2, 67.1, 65.8, 64.0, 65.1, and 65.3 (grams
per liter).
(a) Reading down and left to right, draw a time series plot of
(a) Calculate the sample mean. Suppose that the desirable
all the data and comment on any features of the data that
value for this solution has been specified to be 65.0
are revealed by this plot.
grams per liter. Do you think that the sample mean
(b) Consider the notion that the first 40 observations were
value computed here is close enough to the target value
generated from a specific process, whereas the last 40 ob-
to accept the solution as conforming to target? Explain
servations were generated from a different process. Does
your reasoning.
the plot indicate that the two processes generate similar
(b) Calculate the sample variance and sample standard
results?
deviation.
(c) Compute the sample mean and sample variance of the first
(c) Suppose that in measuring the concentration, the operator
40 observations; then compute these values for the second
must set up an apparatus and use a reagent material. What
40 observations. Do these quantities indicate that both
do you think the major sources of variability are in this ex-
processes yield the same mean level? The same variabil-
periment? Why is it desirable to have a small variance of
ity? Explain.
these measurements?
6-74. A sample of six resistors yielded the following resist- 6-77. Reconsider the data from Exercise 6-76. Prepare
comparative box plots for two groups of observations: the
ances (ohms): x 1 45, x 2 38, x 3 47, x 4 41, x 5 35,
first 40 and the last 40. Comment on the information in the
and x 6 43.
box plots.
(a) Compute the sample variance and sample standard
deviation. 6-78. The data shown in Table 6-7 are monthly champagne
(b) Subtract 35 from each of the original resistance measure- sales in France (1962-1969) in thousands of bottles.
ments and compute s 2 and s. Compare your results with (a) Construct a time series plot of the data and comment on
those obtained in part (a) and explain your findings. any features of the data that are revealed by this plot.
(c) If the resistances were 450, 380, 470, 410, 350, and 430 (b) Speculate on how you would use a graphical proce-
ohms, could you use the results of previous parts of this dure to forecast monthly champagne sales for the year
2
problem to find s and s? 1970.
6-75. Consider the following two samples: 6-79. A manufacturer of coil springs is interested in imple-
menting a quality control system to monitor his production
Sample 1: 10, 9, 8, 7, 8, 6, 10, 6 process. As part of this quality system, it is decided to record
Sample 2: 10, 6, 10, 6, 8, 10, 8, 6 the number of nonconforming coil springs in each production