Page 347 - Fundamentals of Probability and Statistics for Engineers

330 Fundamentals of Probability and Statistics for Engineers

:
:
Since d 2 < c 10, 0 05: , we accept normal distribution N(30 3, 3 14) at the 5% sig-
nificance level.
Let us remark that, since the parameter values were also estimated from the
data, it is more appropriate to compare d 2 with a value somewhat smaller than
0.41. In view of the fact that the value of d 2 is well below 0.41, we are safe in
making the conclusion given above.

REFERENCES

Beard, L.R., 1962, Statistical Methods in Hydrology, Army Corps of Engineers, Sacra-
mento, CA.

 e
Cram r, H., 1946, Mathematical Methods of Statistics, Princeton University Press,

Princeton, NJ.
Fisher, R.A., 1922, ‘‘On the Interpretation of 2 from Contingency Tables, and Calcula-
tions of P’’, J. Roy. Stat. Soc. 85 87–93.

Fisher, R.A., 1924, ‘‘The Conditions under which 2 Measures the Discrepancy between
Observation with Hypothesis’’, J. Roy. Stat. Soc. 87 442–476.

Massey, F.J., 1951, ‘‘The Kolmogorov Test for Goodness of Fit’’, J. Am . Stat. Assoc. 46
68–78.
Pearson, K., 1900, ‘‘On a Criterion that a System of Deviations from the Probable in the
Case of a Correlated System of Variables is such that it can be Reasonably Supposed
to have Arisen in Random Sampling’’, Phil. Mag. 50 157–175.

FURTHER READING AND COMMENTS

We have been rather selective in our choice of topics in this chapter. A number
of important areas in hypotheses testing are not included, but they can be found
in more complete texts devoted to statistical inference, such as the following:
Lehmann, E.L., 1959, Testing Statistical Hypotheses, John Wiley & Sons Inc. New York.

PROBLEMS

10.1 In the 2 test, is a hypothesized distribution more likely to be accepted at ˆ :
0 05
than at ˆ :
0 01? Explain your answer.
10.2 To test whether or not a coin is fair, it is tossed 100 times with the following
outcome: heads 41 times, and tails 59 times. Is it fair on the basis of these tosses at
the 5% significance level?
10.3 Based upon telephone numbers listed on a typical page of a telephone directory,
test the hypothesis that the last digit of the telephone numbers is equally likely to be
any number from 0 to 9 at the 5% significance level.
10.4 The daily output of a production line is normally distributed with mean m ˆ 8000
items and standard deviation ˆ 1000 items. A second production line is set up,

TLFeBOOK