6, 7 Lottery Results Many states have a Pick 3 lottery in which three digits are

Question

6, 7

Lottery Results Many states have a Pick 3 lottery in which three digits are randomly selected each day. Winning requires that you select the same three digits in the same order that they are drawn. Assume that you compute the mean of each set of three selected digits. a. What is the approximate shape of the distribution of the sample means (uniform, normal, skewed, other)? b. What value do the sample means target? That is, what is the mean of all such sample means? c. For each set of three digits that is selected, if you find the proportion of odd numbers, what is the mean of those proportions? In Exercises 7-10, use the same population of {4, 5, 9} that was used in Examples 1 and 5. As in Examples 1 and 5, assume that samples of size n = 2 are randomly selected with replacement. Sampling Distribution of the Sample Variance a. Find the value of the population variance signa^2. b. Table 6-3 describes the sampling distribution of the sample mean. Construct a similar table representing the sampling distribution of the sample variance s^2. Then combine values of s^2 that are the same, as in Table 6-4. c. Find the mean of the sampling distribution of the sample variance. d. Based on the preceding results, is the sample variance an unbiased estimator of the population variance? Why or why not?

Explanation / Answer

Answer to question# 6)

a) The smapling mean will surely have a normal distribution

b) The sample mean defiinitely aims to target the population mean. It depends on the sample size on how close it gets to the true population mean

c) Again in this case when we look for proportion of odd numbers, the proportion of odd numbers will be equal to the proportion of even numbers. Theoretically it must be equal to 0.5. But practically it must be close to 0.5.

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