In the Chips Ahoy cookie example (Exercise 6), a \(95 \%\) confidence interval with a width of approximately 100 (the difference between the lower limit of \(1,204.30\) and the higher limit of \(1,317.70\) ) was constructed when the sample consisted of 18 bags of cookies \((N=18)\). Using the standard deviation of 114.01 as the estimate of the population standard deviation ( \(\hat{\sigma}\) ) \(\ldots\)

a. How large should the sample be for a desired \(95 \%\) confidence interval width of 50 chocolate chips?

b. How large should the sample be for a desired \(95 \%\) confidence interval width of 30 chocolate chips?

c. How large should the sample be for a desired \(95 \%\) confidence interval width of 10 chocolate chips?