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.
(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
--------------
Critical value for 2-tail test with alpha = 1%: +/- 2.5758..
---------------
Test statistic: z(28/60) = [(28/60)-0.5]/[0.5*0.5/sqrt(60)] = -1.0328
------------------
Conclusion: Since TS is not in the rejection interval, Fail to Reject Ho.
The test provides evidence that the coin is not biased.
=================
(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%
----------
Interpretation: Apporximately 30% of test results could have provided
stronger evidence for rejecting Ho, i.e. that the coin is biased.
===========================
Cheers,
Stan H.
|
|
|
