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# The shade.norm.c function (provided at the end of this document) requires you to input the SE of the sample average.

INSTRUCTIONS TO CANDIDATES

PROBLEM 4: theoretical analysis, parameters vs statistics

(a) Discuss what happens as the sample size increases in parts a, b, c of problems 1-3. (b)Discuss what role, if any, the population type had on whether the sample sums and averages are approximately normally distributed. (c)A parameter is a numerical fact about a population or distribution. A statistic is a number computed from a sample. Given a population to analyze, parameters are constants and the same for everyone, but different samples yield different statistics. For Problem 1 (a,b,c), make a table (in Word or R) that compares the true expected values and standard errors with their corresponding estimates from your samples. Discuss whether they are the same, similar, or different, and what affects this.

(d)Regarding the Central Limit Theorem, which of these things are approximately normal: the population, the sample, the sum of the sample, the average of the sample?

PROBLEM 5: z-interval with normal curve plot

The shade.norm.c function (provided at the end of this document) requires you to input the SE of the sample average. Modify this function in R so that it computes the SE for you. That is, modify the function so that it takes the following four inputs (you choose the order and the names):

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