What is the p-value for this sample? (Report answer accurate to four decimal places.) p-value =

Question

You wish to test the following claim (Ha) at a significance level of a=0.10.

      Ho:p=0.16

      Ha:p>0.16

You obtain a sample of size n=522 in which there are 110 successful observations. For this test, you should use the (cumulative) binomial distribution to obtain an exact p-value. (Do not use the normal distribution as an approximation for the binomial distribution.)

Answer 1

p-value is the probability that you would obtain the observed result or a more "extreme" result if the null hypothesis were in fact true. I presume from the wording of this question that you have access to software that will compute the cumulative probabilities for the binomial distribution. The BINOM.DIST function in Excel will compute them. To answer this question you want the probability of obtaining 110 or more successes in 522 trials if the probability of success on a single trial is 0.16 (the value under the null hypothesis.) Using the R language, I would compute that this way:

1 - pbinom(109, 522, 0.16)

The pbinom() function (and the BINOM.DIST function in Excel) by default returns the cumulative probability to the left, but in this case, for 110 or more successes, we want the probability in the right tail, so I subtract the probability from one. Note that I have set the probability of successes to 109, because that will leave 110 or more successes in the right tail, which is what we want in this case.