I believe the binom.test procedure is producing one tailed p values
rather than the two tailed value implied by the alternative hypothesis
language.  A textbook and SAS both show 2*9.94e-07 = 1.988e-06 as the
two tailed value.  As does the R summation syntax from R below.  It
looks to me like the alternative hypothesis language should be revised
to something like " ... greater than or equal to ..."  Am I mistaken?

 

M.C.Grant

 

> 2*sum(dbinom(c(10:25),25,0.061))

[1] 1.987976e-06

 

> binom.test(10,25,0.061)

 

        Exact binomial test

 

data:  10 and 25 

number of successes = 10, number of trials = 25, p-value = 9.94e-07

alternative hypothesis: true probability of success is not equal to
0.061 

95 percent confidence interval:

 0.2112548 0.6133465 

sample estimates:

probability of success 

                   0.4


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