Question

Suppose you are a fourth grade teacher. Your students have all gone trick-or-treating for Halloween. You had them keep track of how many pieces of candy they collected in the first hour of trick-or-treating. You know that the amount of candy that a student receives is Normally distributed. On average, the 100 students in fourth grade had 48 pieces of candy.

a. Assume that you know σ^2 = 81 pieces of candy squared, construct a 90 percent confidence interval for the population mean.

b. Now assume you don’t know σ^2 but you know s^2 = 81 pieces of candy squared. Find the new 90 percent confidence interval.

c. Did you need to use the Central Limit Theorem in part (b)? Explain.

d. Suppose that we did not know that the distribution of candy was Normally distributed. Does it matter for our ability to use the formulas in parts (a) and (b) in this case? In general? Explain clearly.

Answer 1