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

Mean yield Standard No of

(In tones). Deviation Hectare

Paddy 80 10 120

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.

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