Refer to Exercise 11. Ten more welds will be made in order to increase the precision of the confidence interval. Which would increase the precision the most, cooling all 10 welds at the rate of 10°C/s, cooling all 10 welds at the rate of 30°C/s, or cooling 5 welds at 10°C/s and 5 at 30°C/s? Explain.

What will be an ideal response?


The standard deviation of the difference between the means is

If all 10 new welds are cooled at 10°C, then

The standard deviation of the difference between the means is then

If all 10 new welds are cooled at 30°C, then

The standard deviation of the difference between the means is then

If 5 of the new welds are cooled at 10°C and 5 at 30°C, then

The standard deviation of the difference between the means is then

Therefore the confidence interval would be most precise if all 10 new welds were cooled at 10°C.

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