Posted by Robert on Sunday, June 6, 2010 at 3:34pm.
Here is one way you might do this problem:
Null hypothesis is that the coin is fair. Ho: p = .5
Alternate hypothesis is that the coin is unfair. Ha: p not equal to .5
Using the binomial formula: P(x) = (nCx)(p^x)[q^(n - x)]
...where n = number of coin tosses, x = number of times came up heads, p = probability given in the null hypothesis, q = 1 - p.
Using your data:
P(38) = (60C38)(.5^38)(.5^22) = ?
I'll let you finish the calculation.
If the alternate hypothesis uses "not equal to" then you multiply the result of the calculation by 2.
Reject the null hypothesis if the test statistic above is less than .10 (significance level); otherwise, do not reject null.
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