in Example 9.18. USE YOUR KNOWLEDGE 9.19 Is the coin fair? In Example 4.3 (page
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Question
in Example 9.18. USE YOUR KNOWLEDGE 9.19 Is the coin fair? In Example 4.3 (page 234) we learned that the South times while imprisoned by the Germans during World War II. The coin came up heads 5067 times. (a) Formulate the question about whether or not the coin was fair as a goodness-of-fit hypothesis. (b) Perform the chi-square significance test and write a short summary of the results. SECTION 9.2 Summary istribu- square goodness-of-fit test is used to compare the sample distribu ion The data for n observations with k possible outcomes are sneifies prob observed counts, ni,n.. n, in k cells. The null hypothesis abilities pi,p2,... p for the possible outcomes. tion of a categorical variable from a population with a hypothesiz e summarized as tables dis- The analysis of these data is similar to the analyses of two-way ted by cussed in Section 9.1. For each cell, the expected count is dete multiplying the total number of observation The null hypothesis i s determinExplanation / Answer
Ans:
H0:Coin was fair i.e. number of heads equals 5000 as expected
H1:Coin was not fair i.e. number of heads not equals 5000 as expected.
Observed count=5067
Expected count=10000*0.5=5000
Test statistic:
Chi square score=(Observed-Expected)2/Expected=(5067-5000)2/5000=0.8978
critical chi square score=3.84
As,calculated chi square score=0.8978<3.84,we fail to reject null hypothesis.
There is sufficient evidence to suggest that coin was fair.
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