How to interpret p-value in this problem. The following is the question in particular, I got this question wrong. However nothing I run across explains why it is wrong. I answered C because with a p-value of 0.087 we don't have an "unusual" enough outcome to reject the null though the correct terminology would be "extreme".
Thank you for your time.

Use the following information to answer the question. A janitor at a large office building believes that his supply of light bulbs has too many defective bulbs. The janitor's null hypothesis is that the supply of light bulbs has a defect rate of p = 0.07 (the light bulb manufacturer's stated defect rate). Suppose he does a hypothesis test with a significance level of 0.05. Symbolically, the null and alternative hypothesis are as follows: H0: p = 0.07 and 
The janitor calculates a p-value for the hypothesis test of approximately 0.087. Choose the correct interpretation for the p-value.
A) The p-value tells us that the true population rate of defective light bulbs is approximately 0.087.
B) None of these
C) The p-value tells us that if the defect rate is 0.07, then the probability that the janitor will have 27 defective light bulbs out of 300 is approximately 0.087. At a significance level of 0.05, this would not be an unusual outcome.
D) The p-value tells us that the probability of concluding that the defect rate is equal to 0.07, when in fact it is greater than 0.07, is approximately 0.087.
 A: You are confusing two different uses of "p" in this problem.
First, p = 0.07 is the proportion of defective light bulbs (the stated defect rate). It simply means that the probability of a randomly selected bulb being defected is 0.07.
Second, the p-value of the hypothesis test is given as 0.087. This means that the janitor has conducted a test. Typically this would be by choosing a certain number of bulbs and seeing how many work. The p-value is as you have described - a measure of how unlikely the observed number of defective bulbs is. In this case you should have the alternative hypothesis $H_1: p>0.07$ so for the p-value is the probability that there are the observed number of faulty light bulbs or more. We aren't told how many he tests or how many faulty bulbs he finds - just the p-value.
So this p-value tells us that the chance of having the observed number of defective bulbs or more is 0.087. Because this is greater than the 5% significance level, we conclude that there is insufficient evidence to support the janitor's claim ($H_1$) and we continue to believe that the defect rate is 0.07.
Answer is "B"
