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Refer to the following list of numbers of | Ch 12.3 - 10 CRE

Elementary Statistics | 12th Edition | ISBN: 9780321836960 | Authors: Mario F. Triola ISBN: 9780321836960 18

Solution for problem 10 CRE Chapter 12.3

Elementary Statistics | 12th Edition

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Elementary Statistics | 12th Edition | ISBN: 9780321836960 | Authors: Mario F. Triola

Elementary Statistics | 12th Edition

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Problem 10 CRE

Problem  10CRE

Refer to the following list of numbers of years that U.S. presidents, popes, and British monarchs lived after their inauguration, election, or coronation, respectively. (As of this writing the last president is Gerald Ford, the last pope is John Paul II, and the last British monarch is George VI.) Assume that the data are samples randomly selected from larger populations.

Lottery: Goodness-of-Fit The bars in the histogram included with Exercise depict these frequencies: 21, 19, 15, 18, 24, 18, 16, 24, 30, and 15- Test the claim that the digits are selected from a population in which the digits are all equally likely. Is there a problem with the lottery?

Exercise

Refer to the following list of numbers of years that U.S. presidents, popes, and British monarchs lived after their inauguration, election, or coronation, respectively. (As of this writing the last president is Gerald Ford, the last pope is John Paul II, and the last British monarch is George VI.) Assume that the data are samples randomly selected from larger populations.

Lottery: Interpreting a Graph Shown below is a histogram of digits selected in California’s Win 4 lottery. Each drawing involves the random selection (with replacement) of four digits between 0 and 9 inclusive.

a. If the lottery works correctly, what should be the shape of the histogram in the long run? Does the histogram shown here depict the expected distribution?

b. Does the display depict a normal distribution? Why or why not?

Step-by-Step Solution:

Answer:

Step 1 of 2</p>

The hypotheses can be written as

H0 : The digits are selected from a population in which the digits are all equally likely

H1 : At least one of the digits selected from a population in which the digits are not equally likely.

Use a 0.05 significance level

SL. No.

O

p = 1/10

E = np

(O - E )2

(O - E)2/E

1

21

0.1

20

1

0.05

2

19

0.1

20

1

0.05

3

15

0.1

20

25

1.25

4

18

0.1

20

4

0.2

5

24

0.1

20

16

0.8

6

18

0.1

20

4

0.2

7

16

0.1

20

16

0.8

8

24

0.1

20

16

0.8

9

30

0.1

20

100

5

10

15

0.1

20

25

1.25

Sum

200

1

200

208

10.4

Expected frequency (E) = np

                                       = 200(1/10)

                                       = 20

The calculation continues as follows. Letting E be the expected frequency of an outcome and O be the observed frequency of that outcome.

Step 2 of 2

Chapter 12.3, Problem 10 CRE is Solved
Textbook: Elementary Statistics
Edition: 12
Author: Mario F. Triola
ISBN: 9780321836960

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