Time taken to solve a math programming problem. Refer to the IEEE Transactions study of a new hybrid algorithm for solving polynomial 0/1 mathematical programs, presented in Exercise. (Data on solution times are saved in the MATHCPU file.) A SAS printout giving descriptive statistics for the sample of 52 solution times is reproduced at the bottom of the page. Use this information to determine whether the variance of the solution times differs from 2. Use α =.05.
Time to solve a math programming problem. IEEE Transactions presented a hybrid algorithm for solving a polynomial zero-one mathematical programming problem. The algorithm incorporates a mixture of pseudo-Boolean concepts and time-proven implicit enumeration procedures. Fifty-two random problems were solved by the hybrid algorithm; the times to solution (CPU time in seconds) are listed in the accompanying table and saved in the MATHCPU file.
a. Estimate, with 95% confidence, the mean solution time for the hybrid algorithm. Interpret the result.
b. How many problems must be solved to estimate the mean μ to within .25 second with 95% confidence?
c. Form a 95% confidence interval for the true standard deviation of the solution times for the hybrid algorithm. Interpret the result.
.045 | 1.055 | .136 | 1.894 | .379 | .136 | .336 | .258 | 1.070 |
.506 | .088 | .242 | 1.639 | .912 | .412 | .361 | 8.788 | .579 |
1.267 | .567 | .182 | .036 | .394 | .209 | .445 | .179 | .118 |
.333 | .554 | .258 | .182 | .070 | 3.985 | .670 | 3.888 | .136 |
.091 | .600 | .291 | .327 | .130 | .145 | 4.170 | .227 | .064 |
.194 | .209 | .258 | 3.046 | .045 | .049 | .079 |
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Source: Snyder, W. S., and Chrissis, J. W. “A hybrid algorithm for solving zero- one mathematical programming problems.” IEEE Transactions, Vol. 22, No. 2, June 1990. Copyright © 1990. IEEE Reprinted with permission.
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