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The force acting on a beam was measured under the same operating conditions and a sample of 5 data points was collected. This process was repeated by 3 observers. The pooled standard deviations of these 3 data sets was 1.21. Determine the true mean force using all pooled data (with a 95% probability). The result should look like this: True mean = mean +/- Margin of Error

Answer :

batolisis

Answer:

± 1.51

Explanation:

The mean standard deviation = 1.21 since the three data sets had 1.21 standard deviations each

95% probability = 0.95

calculate standard error is calculated as = [tex]\sqrt{MSE}[/tex] = [tex]\sqrt{\frac{SSE}{N-K} }[/tex]

[tex]\sqrt{\frac{(n-1)s^2}{15-3} }[/tex]=  [tex]\sqrt{\frac{4(1.2)^2}{12} }[/tex]

=  [tex]\sqrt{\frac{5.76}{12} }[/tex]  = [tex]\sqrt{0.48}[/tex]  =  0.6928

calculate the margin of error

[tex]tan_{0.05/2.12} * se[/tex]

from statistical table equation  becomes

2.179 * 0.6928 = 1.5096 ≈   ± 1.51

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