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# Solved: Flipping and Spinning Pennies Use the data in the ISBN: 9780321836960 18

## Solution for problem 5 RE Chapter 11.3

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:

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

##### ISBN: 9780321836960

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