# Math and Science Solutions for Businesses/Help me for assignment

Question
Productivity test of two articles- paddy and wheat given the following result

Mean yield    Standard        No of
(In tones).    Deviation       Hectare

Wheat        75          12          90

Is the difference between standard deviation is significant?

Sofi,

To compare variances, you need to use the F distribution. FYI, this is the distribution of the ratio of the 2 variances you are comparing (which are presumably chi-square distributed). You also need to specify the number of degrees of freedom assumed in the calculation of the variances. Together these give the statistic

F = [ V1/n1 ] / [ V2/n2 ].       V1 = variance of 1st sample, n1 = degrees of freedom for 1st, etc.

Although it doesn't really say so explicitly, I'm going to assume that the number of hectares corresponds to the number of degrees of freedom. Thus (with the higher variance going on top),

F = (12/90)/(10/120) = 1.59.

Now we need to look up value of F in a table to determine if this value of F is large enough to reject the null hypothesis (i.e., H0 = variances are the same) at a specified confidence level, α. Since we are interested in whether the variances are just different, i.e., not assuming one is strictly greater than the other, we use a 2-tailed test.

Looking at a table for α = 0.05, I get

F_table = 1.47 for n1 = 90,   n2 = 120 and
F_table = 1.35 for n1 = 120, n2 = 120

Interpolating between n1=90 and n1=120, I get F_table = 1.41. Since the F calculated from the data, 1.59, is greater than 1.41, we can conclude that the variances are different at the 10% level of confidence (its 10% and not 5% because this is a 2-tailed test whereas the tables are for 1-tailed).

Hope this helps.

Math and Science Solutions for Businesses

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#### Randy Patton

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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.

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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.

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

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

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