Chapter 12: Sec 7.3 Signs test

In the example on page 38 where they calculate the test statistic for the Signs test, why do we calculate the p-value as 2*P(P<=6) and not 2*P(P>=6)?

I always think of p-values are the value on the tails.

 

Question 12.11a

The solution used P(>=27 negative values) and concluded that graduated rates are higher than observed because the two tailed p-value is 4%.

How should I change my interpretation of the results, if I had used the 13 positive values instead?

 

Question 12.11b

Again, the solution here is contradicting with the solution to the example shown on page 38 of this chapter.

In the example, p-value is calculated based on P(=<6 positive values) but in solution 12.11 the p-value is calculated based on P(>= 5 positive values). Which one is it suppose to be???