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Elementary Statistics | 12th Edition | ISBN: 9780321836960 | Authors: Mario F. Triola
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Solved: In Exercises, use the population of ages {56, 49,

Chapter 6, Problem 12BSC

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QUESTION:

In Exercises 11–14, use the population of ages {56, 49, 58, 46} of the four U.S. presidents (Lincoln, Garfield, McKinley, Kennedy) when they were assassinated in office. Assume that random samples of size n = 2 are selected with replacement.

Sampling Distribution of the Median Repeat Exercise 11 using medians instead of means.

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QUESTION:

In Exercises 11–14, use the population of ages {56, 49, 58, 46} of the four U.S. presidents (Lincoln, Garfield, McKinley, Kennedy) when they were assassinated in office. Assume that random samples of size n = 2 are selected with replacement.

Sampling Distribution of the Median Repeat Exercise 11 using medians instead of means.

ANSWER:

Answer:

Step 1 of 2

a. Here, the sample median is the middlemost values of the ordered list.

Add the probabilities for each sample value.

Thus the second table is the sampling distribution

Sample

Sample Median

Probability

56, 56

56

1/16

56, 49

52.5

1/16

56, 58

57

1/16

56, 46

51

1/16

49, 56

52.5

1/16

49, 49

49

1/16

49, 58

53.5

1/16

49, 46

47.5

1/16

58, 56

57

1/16

58, 49

53.5

1/16

58, 58

58

1/16

58, 46

52

1/16

46, 56

51

1/16

46, 49

47.5

1/16

46, 58

52

1/16

46, 46

46

1/16

Sample Median

Probability

46

1/16 = 0.0625

47.5

2/16 = 0.125

49

1/16 = 0.0625

51

2/16 = 0.125

52

2/16 = 0.125

52.5

2/16 = 0.125

53.5

2/16 = 0.125

56

1/16 = 0.0625

57

2/16 = 0.125

58

0.0625

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