Question 278536: I have been staring at this for hours and have no clue how to solve it Can you please help?
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)   (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.
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