Question 174374
A coin was flipped 60 times and came up heads 38 times.
(a) At the .10 level of significance, is the coin biased toward heads? Show your decision rule and calculations.
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Ho: p = 1/2
Ha: p is not 1/2
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Critical value for 2-tail test with alpha = 1%: +/- 2.5758..
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Test statistic: z(28/60) = [(28/60)-0.5]/[0.5*0.5/sqrt(60)] = -1.0328
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Conclusion: Since TS is not in the rejection interval, Fail to Reject Ho.
The test provides evidence that the coin is not biased.
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(b) Calculate a p-value and interpret it.
P(z<-1.0328) = 0.150845
Since this is a 2-tail test the p-value is 2(0.150845) or appox. 30%
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Interpretation: Apporximately 30% of test results could have provided
stronger evidence for rejecting Ho, i.e. that the coin is biased.
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Cheers,
Stan H.