Question 1104827: Students conducted an experiment to determine whether the Belgium-minted Euro coin was equally likely to land heads up or tails up. Coins were spun on a smooth surface, and in 270 spins, 150 landed with the heads side up.
(a) Should the students interpret this result as convincing evidence that the proportion of the time the coin would land heads up is not 0.5? Test the relevant hypotheses using α = 0.01. (Round your test statistic to two decimal places and your P-value to four decimal places.)
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Students conducted an experiment to determine whether the Belgium-minted Euro coin was equally likely to land heads up or tails up. Coins were spun on a smooth surface, and in 270 spins, 150 landed with the heads side up.
(a) Should the students interpret this result as convincing evidence that the proportion of the time the coin would land heads up is not 0.5? Test the relevant hypotheses using α = 0.01. (Round your test statistic to two decimal places and your P-value to four decimal places.)
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Ho: p = 0.5
Ha: p # 0.5
Sample proportion = 150/270 = 5/9
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Test statistic::z(5/9) = (5/9-1/2)/sqrt[0.5*0.5/270] = 1.8257
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p-value = 2*P(z > 1.8257) = 2*normalcdf(1.8257,100) = 0.67
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Conclusion: Since the p-value is > 0.01, fail to reject Ho
Conclusion: Test result supports the conclusion that p = 0.5
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Cheers,
Stan H.
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