Question

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 1

± 1.51

Step-by-step 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 =
`√(MSE)` =
`\sqrt{(SSE)/(N-K) }`

`\sqrt{((n-1)s^2)/(15-3) }`=
`\sqrt{(4(1.2)^2)/(12) }`

=
`\sqrt{(5.76)/(12) }` =
`√(0.48)` = 0.6928

calculate the margin of error

`tan_(0.05/2.12) * se`

from statistical table equation becomes

2.179 * 0.6928 = 1.5096 ≈ ± 1.51