SOLUTION: 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. (b) Calcul

Algebra ->  Probability-and-statistics -> SOLUTION: 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. (b) Calcul      Log On


   

Question 136488: 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. (b) Calculate a p-value and
interpret it.
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
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.
Ho: p=1/2
Ha: p is not 1/2
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p-hat = 38/60 = 0.63333...
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Critical value for 2-tail z-test with alpha = 10%: z = +/- 1.645
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Test statistic:
z(0.633333) = (0.6333-0.5)/sqrt[(0.5)(0.5)/60] = 0.13333/0.064549..= 2.0656
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(b) Calculate a p-value and interpret it.
p-value = P(2.0656 < z < 10 ) = 2*0.019434..= 0.03887..
Interpretation: Only 0.03887 of test results could have given
stronger evidence for rejecting Ho.
Conclusion: Since p-value < alpha, reject Ho.
This is statistical evidence that the coin is biased.
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Cheers,
Stan H.