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The probability distribution shown here describes a

Statistics for Business and Economics | 12th Edition | ISBN: 9780321826237 | Authors: James T. McClave, P. George Benson, Terry T Sincich ISBN: 9780321826237 51

Solution for problem 1E Chapter 5

Statistics for Business and Economics | 12th Edition

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Statistics for Business and Economics | 12th Edition | ISBN: 9780321826237 | Authors: James T. McClave, P. George Benson, Terry T Sincich

Statistics for Business and Economics | 12th Edition

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Problem 1E

        Problem 1E

The probability distribution shown here describes a population of measurements that can assume values of 0, 2, 4, and 6, each of which occurs with the same relative frequency:

x

0

2

4

6

p(x)

¼

¼

¼

1/4

a. List all the different samples of n = 2 measurements that can be selected from this population.

b. Calculate the mean of each different sample listed in part a.

c. If a sample of n = 2 measurements is randomly selected from the population, what is the probability that a specific sample will be selected?

d. Assume that a random sample of n = 2 measurements is selected from the population. List the different values of x̄found in part b and find the probability of each. Then give the sampling distribution of the sample mean x̄ in tabular form.

e. Construct a probability histogram for the sampling distribution of x̄.

Step-by-Step Solution:

Answer:

Step 1 of 6:

Given the probability distribution describes a population of measurements that can assume values of 0, 2, 4 and 6 each of which occurs with the same relative frequency.

       

     x

  0

2

4

6

 

   p(x)

 

   

Step 2 of 6:  

a). To list all the different samples of n = 2 measurements that can be selected from this population.

       The different samples of n = 2 with replacement and their means are:

                       

  Possible samples

  (0,0)

(0,2)

(0,4)

(0,6)

(2,0)

(2,2)

(2,4)

(2,6)

(4,0)

(4,2)

(4,4)

(4,6)

(6,0)

(6,2)

(6,4)

(6,6)

 Step 3 of 6:

 b). To calculate the mean of each different sample listed in part(a).

       

  Possible samples

 Mean (

  (0,0)

0

(0,2)

1

(0,4)

2

(0,6)

3

(2,0)

1

(2,2)

2

(2,4)

3

(2,6)

4

(4,0)

2

(4,2)

3

(4,4)

4

(4,6)

5

(6,0)

3

(6,2)

4

(6,4)

5

(6,6)

6

 

Step 4 of 5

Chapter 5, Problem 1E is Solved
Step 5 of 5

Textbook: Statistics for Business and Economics
Edition: 12
Author: James T. McClave, P. George Benson, Terry T Sincich
ISBN: 9780321826237

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