8.1

Consider the following population: {1,2,2,3,3}. The value ofis2.2, but suppose that this is not known to an investigator. Three possible statistics for estimatingare

• Statistic 1: the sample mean,x
• Statistic 2: the sample median
• Statistic 3: the average of the largest and the smallest values in the sample

A random sample of size 3 will be selected without replacement. Provided that we disregard the order in which the observations are selected, there are 10 possible samples that might result (writing2and2*,3and3* to distinguish the two2's and the two3's in the population.)

1,2,2*

1,2,3

1,2,3*

1,2*,3

1,2*,3*

1,3,3*

2,2*,3

2,2*,3*

2,3,3*

2*,3,3*

(a)

For each of these 10 samples, calculate the values of Statistics 1, 2, and 3. (For each answer, enter an exact number as an integer, fraction, or decimal.)

(c)

Which statistic would you recommend for estimating? Explain your reasoning. (For each answer, enter an exact number as an integer, fraction, or decimal.)

Using the sampling distributions above, the means of the three statistics are calculated to beE(Statistic 1) =,E(Statistic 2) =,andE(Statistic 3) =.