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Solved: Flipping and Spinning Pennies Use the data in the

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

Solution for problem 5 RE Chapter 11.3

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 5 RE

Problem  5RE

Flipping and Spinning Pennies Use the data in the table below with a 0.05 significance level to test the claim that when flipping or spinning a penny, the outcome is independent of whether the penny was flipped or spun. (The data are from experimental results given in Chance News)Does the conclusion change if the significance level is changed to 0.01?

 

Heads

Tails

Flipping

2048

1992

Spinning

953

1047

Step-by-Step Solution:

Answer:

Step 1 of 2</p>

 

Heads

Tails

Total

Flipping

2048

1992

4040

Spinning

953

1047

2000

Total

3001

3039

6040

The solution to this problem takes four steps: (1) state the hypotheses, (2) formulate an analysis plan, (3) analyze sample data, and (4) interpret results. We work through those steps below:

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

H0: The claim that when flipping or spinning a penny, the outcome is independent

H1: The claim that when flipping or spinning a penny, the outcome is not independent

Formulate an analysis plan. For this analysis, the significance level is 0.05. Using sample data, we will conduct a chi-square test for independence.

Applying the chi-square test for independence to sample data, we compute the degrees of freedom, the expected frequency counts, and the chi-square test statistic.

DF = (r - 1)  (c - 1) = (2 - 1)  (2 - 1) = 1

 

Heads

Tails

Total

Flipping

2048

1992

4040

Spinning

953

1047

2000

Total

3001

3039

6040

= 2007.2913

= 2032.7086

= 993.7086

= 1006.2913

SL.No

O

E

(O - E )2

(O - E)2/E

1

2048

2007.2913

1657.198

0.825589318

2

1992

2032.7086

1657.19

0.815262017

3

953

993.7086

1657.19

1.66768217

4

1047

1006.2913

1657.198

1.646837507

Sum

6040

6039.9998

6628.777

4.955371012

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 11.3, Problem 5 RE is Solved
Textbook: Elementary Statistics
Edition: 12
Author: Mario F. Triola
ISBN: 9780321836960

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Solved: Flipping and Spinning Pennies Use the data in the

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