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An analysis of a pesticide in soil came out to be 1.5 (+- 0.5) %(w/w) from...

An analysis of a pesticide in soil came out to be 1.5 (+- 0.5) %(w/w) from a set of 11 measurements. Another set of 11 measurements gave 1.6 (+- 0.4) %(w/w). What would be the value of the standard deviation if the data was pooled?
Math   Statistics-And-Probability   
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Answer #1

The mean and the confidence interval for the sample 1 is 1.5 and (1.5-0.5, 1.5+0.5).

The mean and the confidence interval for the sample 2 is 1.5 and (1.6-0.4, 1.6+0.4).

The formula for confidence interval is

Where is the sample mean, ta is the t critical value at the alpha level of significance, S is the sample standard deviation and n is sample size.

Therefore for sample 1,   

At 5% level of significance, ta = 1.96 and n = 11. Hence, => S1 = 0.8461.

Similarly, S2 = 0.6769.

The formula for pooled standard deviation is

Where:

  • x̄ = the sample mean
  • n1 = sample size for sample 1
  • n2 = sample size for sample 2
  • SD1 = standard deviation for sample 1
  • SD1 = standard deviation for sample 2

Therefore,

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