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In: Statistics and Probability

6. Enthalpy is a measure of total energy in a thermodynamic system. The following table presents...

6. Enthalpy is a measure of total energy in a thermodynamic system. The following table presents enthalpy measurements on 16 water based systems. Four measurements are made on each of four systems which differ by concentration of NaCl (table salt).

Concentration (%)

Enthalpy

5

1.62

1.60

1.62

1.66

10

2.69

2.66

2.72

2.73

20

3.56

3.45

3.65

3.52

30

3.35

3.18

3.40

3.06

  1. What pairs of concentrations, if any, can you conclude to have differing enthalpies? Use α = 0.05.

  

5-10

-1.07

10-5

1.07

20-5

1.92

30-5

1.62

5-20

-1.92

10-20

-0.85

20-10

0.85

30-20

0.55

5-30

-1.62

10-30

-0.55

20-30

0.30

30-10

-0.30

All concentrations are significant at the 0.05 level. WHY?

  1. Compute the quantity s = (MSE)0.5, the estimate of the standard deviation σ.
  1. Assuming s to be the error standard deviation, find the sample size necessary in each treatment to provide a power of 0.80 to detect a maximum difference of 0.1 in the treatment means at the 5% level.

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