Math and Science Solutions for Businesses/Business Statistics


Two research laboratories have independently produced drugs that provide relief to arthritis sufferers. The …first drug was tested on a group of 90 arthritis sufferers and produced an average of 8.5 hours of relief, and a sample standard deviation of 1.8 hours. The second drug was tested on 80 arthritis sufferers, producing an average of 7.9 hours of relief, and a sample standard deviation of 2.1 hours. At the 0.05 level of …significance, does the second drug provide a signifi…cantly shorter period of relief?

This asks for a confidence interval for the difference between 2 means with the standard deviations calculated from the samples. We therefore need to use a one-tailed t-distribution. The standard deviation, SD, for the difference is (with n_1 = # of samples for the first group = 90 and n_2 = 80 for the second)

SD_1,2 = ( SD_1^2/n_1 + SD_2^2/n_2)^1/2 = 0.30

The t-score is thus t = (8.5 - 7.9)/0.30 = 2.0.

With the number of degrees of freedom = (n_1 - 1) + (n_2 - 1) = 168, a table of critical t-values gives a p-value (=probability in the tail of the distribution) of approximately 0.025. Since this is smaller than 0.05, the second drug does provides a shorter period at the 5% level of confidence.

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Randy Patton


Questions regarding application of mathematical techniques and knowledge of physics and engineering principles to product and services design, optimization, prediction, feasibility and implementation. Examples include sales and product performance projections based on math/physics models in addition to standard regression; practical and cost effective sensor design and component configuration; optimal resource allocation using common tools (eg., MS Office); advanced data analysis techniques and implementation; simulation and "what if" analysis; and innovative applications of remote sensing.


26 years as professional physical scientist and project manager for elite research company providing academic quality basic and applied research for government and defense industry clients (currently retired). Projects I have been involved in include: - Notional sensor performance predictions for detecting underwater phenomena - Designing and testing guidance algorithms for multi-component system - Statistical analysis of ship tracking data and development of anomaly detector - Deployed vibration sensors in Arctic ice floes; analysis of data - Developed and tested ocean optical instrument to measure particles - Field testing of protoype sonar system - Analysis of synthetic aperture radar system data for ocean surface measurements - Redesigned dust shelters for greeters at Burning Man Festival Project management with responsibility for allocation and monitoriing of staff and equipment resources.

“A Numerical Model for Low-Frequency Equatorial Dynamics” (with Mark A. Cane), J. of Phys. Oceanogr., 14, No. 12, pp. 18531863, December 1984.

MIT, MS Physical Oceanography, 1981 UC Berkeley, BS Applied Math, 1976

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