What is the p-value of this test?

Question

In a random sample of 400 adult (age 25 or over) US Citizens, 122 of them hold a Bachelor's degree. Let pp be the true proportion of adult US Citizens that hold a Bachelor's degree. Does the sample indicate that pp is other than 0.4? Use a 0.01 level of significance.

Answer 1

122/400=0.305 compared with 0.4. 

t=(0.305-0.4)/√(0.4×0.6/400)=-3.88 approx.

For significance level of 0.01 (2-tail test), critical value is 2.59.

The null hypothesis (that is, no significant difference from pp) is rejected, because the magnitude of 3.88 exceeds 2.59, so it is likely that pp is other than 0.4.