Hypothesis Testing and Finding P-Value

Although 85% of the general public is right-handed, a survey of 300 chief executive officers of large corporations found that 96% were right-handed.

a) Is this difference in percentages statistically significant? Test using α = 0.01.
b) Find the p-value for the test and explain what it means.

Attempt At Solution

a) The rejection region is {z > 2.33}.

Using the test:

z = (p - p0)/(sqrt(p0*(1-p0)/n), where p0 = .85, p = .96, and n = 300

I got z = 5.34. Since 5.34 > 2.33, this lies in the rejection region and thus, the difference is significant.

b) p-value = P(Z > 5.34) = 0.000000287

Since this value is so small, it is evident that the null hypothesis should be rejected.

Is this correct?

It isn't clear to me that the test should be one-sided, but other than that it looks fine.

agreed
it should be clear what you're trying to prove
when I see the word difference, I think of a two-sided test