Question

Consider the population of four juvenile condors. Their weights in pounds are : 4, 5, 7, 12 (a) Let x be the weight of a juvenile condor. Write the possible unique values for x: (NOTE: Separate each value in the list with a comma.) . (b) Find the mean of the population: (c) Let x¯ be the average weight from a sample of two juvenile condors. List all possible outcomes for x¯. (If a value occurs twice, make sure to list it twice.) This is the sampling distribution for samples of size 2: (NOTE: Separate each value in the list with a comma.) . (d) Find the mean of the sampling distribution: Note: You can earn partial credit on this problem.

Answer 1

a) 4, 5, 7, 12

b) 7

c) 4.5, 6.5, 8, 6, 8.5, 9.5

d) 7.167

Explanation:

We are given the following in the question:

4, 5, 7, 12

a) unique values for x

4, 5, 7, 12

b) mean of the population

`Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}`

`\mu =\displaystyle(28)/(4) = 7`

c) sampling distribution for samples of size 2

Sample size, n = 2

Possible samples of size 2 are (4,5),(4,7),(4,12),(5,7),(5,12),(7,12)

Sample means are:

`\bar{x_1} = (4+5)/(2) = 4.5\\\\\bar{x_2} = (4+7)/(2) = 6.5\\\\\bar{x_3} = (4+12)/(2) = 8\\\\\bar{x_4} = (5+7)/(2) = 6\\\\\bar{x_5} = (5+12)/(2) = 8.5\\\\\bar{x_6} = (7+12)/(2) = 9.5`

Thus, the list is 4.5, 6.5, 8, 6, 8.5, 9.5

d) mean of the sampling distribution

`\bar{x} = (4.5 + 6.5 + 8+ 6 + 8.5+ 9.5)/(6) = (43)/(6) = 7.167`