Refer to Exercise 5. Additional pieces of yarn will be sampled in order to improve the precision of the confidence interval. Which would increase the precision the most: sampling 50 additional pieces of yarn from the old batch, 50 additional pieces from the new batch, or 25 additional pieces from each batch?

What will be an ideal response?


The standard deviation for the difference between the means is Estimate

If 50 pieces of yarn are sampled from the old batch, then = 175 and = 75.



The standard deviation for the difference between the means is then



If 50 pieces of yarn are sampled from the new batch, then = 125 and = 125.



The standard deviation for the difference between the means is then



If 25 pieces of yarn are sampled from each batch, then = 150 and = 100.



The standard deviation for the difference between the means is then



Therefore sampling 50 additional pieces from the new batch increases the precision the most.

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