Two tailed test occur when the alternative hypothesis H1 is that the value of p is not equal to a given value. In cases like this the nominal significance level is halved and applied to each tail to locate the rejection regions.
In this next example I demonstrate this
A person suggests that the proportion, p of red cars on a road is 0.3. In a random sample of 15 cars it is desired to test the null hypothesis p = 0.3. against p ≠ 0.3 at a nominal significance level of 10%.
Determine the appropriate acceptance region and the corresponding actual significance level.