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a. Calculate a 95% confidence interval for the population mean µ and interpret your interval in the context of this problem. b. Could we have used the 95% confidence interval calculated in (a) to make a decision about the hypothesis test conducted? Explain why or why not.  c. Engineers would like to engage in a larger study (where new pencils would be sampled) to estimate p = proportion of pencils with ash content greater than 42.5 percent. The goal is to write a 95% percent confidence interval for p whose total length is no greater than 0.06. How many observations should the engineers collect in their study?

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